linear_algebra.span ⟷ Mathlib.LinearAlgebra.Span

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

@@ -4,8 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Frédéric Dupuis,
   Heather Macbeth
 -/
-import LinearAlgebra.Basic
-import Order.CompactlyGenerated
+import Algebra.Module.Submodule.Ker
+import Order.CompactlyGenerated.Basic
 import Order.OmegaCompletePartialOrder
 
 #align_import linear_algebra.span from "leanprover-community/mathlib"@"10878f6bf1dab863445907ab23fbfcefcb5845d0"
@@ -1037,7 +1037,7 @@ instance : IsModularLattice (Submodule R M) :=
     rcases ha with ⟨⟨b, hb, c, hc, rfl⟩, haz⟩
     rw [mem_sup]
     refine' ⟨b, hb, c, mem_inf.2 ⟨hc, _⟩, rfl⟩
-    rw [← add_sub_cancel c b, add_comm]
+    rw [← add_sub_cancel_right c b, add_comm]
     apply z.sub_mem haz (xz hb)⟩
 
 end AddCommGroup
@@ -1225,7 +1225,7 @@ theorem span_singleton_sup_ker_eq_top (f : V →ₗ[K] K) {x : V} (hx : f x ≠
         ⟨y - (f y * (f x)⁻¹) • x, by
           rw [LinearMap.mem_ker, f.map_sub, f.map_smul, smul_eq_mul, mul_assoc, inv_mul_cancel hx,
             mul_one, sub_self],
-          by simp only [add_sub_cancel'_right]⟩⟩
+          by simp only [add_sub_cancel]⟩⟩
 #align linear_map.span_singleton_sup_ker_eq_top LinearMap.span_singleton_sup_ker_eq_top
 -/
 

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

@@ -435,7 +435,7 @@ variable {p p'}
 #print Submodule.mem_sup /-
 theorem mem_sup : x ∈ p ⊔ p' ↔ ∃ y ∈ p, ∃ z ∈ p', y + z = x :=
   ⟨fun h => by
-    rw [← span_eq p, ← span_eq p', ← span_union] at h 
+    rw [← span_eq p, ← span_eq p', ← span_union] at h
     apply span_induction h
     · rintro y (h | h)
       · exact ⟨y, h, 0, by simp, by simp⟩
@@ -496,7 +496,7 @@ theorem nontrivial_span_singleton {x : M} (h : x ≠ 0) : Nontrivial (R ∙ x) :
   ⟨by
     use 0, x, Submodule.mem_span_singleton_self x
     intro H
-    rw [eq_comm, Submodule.mk_eq_zero] at H 
+    rw [eq_comm, Submodule.mk_eq_zero] at H
     exact h H⟩
 #align submodule.nontrivial_span_singleton Submodule.nontrivial_span_singleton
 -/
@@ -580,7 +580,7 @@ theorem disjoint_span_singleton {K E : Type _} [DivisionRing K] [AddCommGroup E]
   obtain ⟨c, rfl⟩ := mem_span_singleton.1 hyx
   by_cases hc : c = 0
   · rw [hc, zero_smul]
-  · rw [s.smul_mem_iff hc] at hy 
+  · rw [s.smul_mem_iff hc] at hy
     rw [H hy, smul_zero]
 #align submodule.disjoint_span_singleton Submodule.disjoint_span_singleton
 -/
@@ -699,9 +699,9 @@ theorem span_singleton_eq_span_singleton {R M : Type _} [Ring R] [AddCommGroup M
   · intro hxy
     cases' mem_span_singleton.mp (by rw [hxy]; apply mem_span_singleton_self) with v hv
     cases' mem_span_singleton.mp (by rw [← hxy]; apply mem_span_singleton_self) with i hi
-    have vi : v * i = 1 := by rw [← one_smul R y, ← hi, smul_smul] at hv ;
+    have vi : v * i = 1 := by rw [← one_smul R y, ← hi, smul_smul] at hv;
       exact smul_left_injective R hy hv
-    have iv : i * v = 1 := by rw [← one_smul R x, ← hv, smul_smul] at hi ;
+    have iv : i * v = 1 := by rw [← one_smul R x, ← hv, smul_smul] at hi;
       exact smul_left_injective R hx hi
     exact ⟨⟨v, i, vi, iv⟩, hv⟩
   · rintro ⟨v, rfl⟩
@@ -786,7 +786,7 @@ theorem iSup_induction {ι : Sort _} (p : ι → Submodule R M) {C : M → Prop}
     (hx : x ∈ ⨆ i, p i) (hp : ∀ (i), ∀ x ∈ p i, C x) (h0 : C 0)
     (hadd : ∀ x y, C x → C y → C (x + y)) : C x :=
   by
-  rw [← mem_to_add_submonoid, supr_to_add_submonoid] at hx 
+  rw [← mem_to_add_submonoid, supr_to_add_submonoid] at hx
   exact AddSubmonoid.iSup_induction _ hx hp h0 hadd
 #align submodule.supr_induction Submodule.iSup_induction
 -/
@@ -1033,7 +1033,7 @@ theorem mem_span_insert' {x y} {s : Set M} :
 
 instance : IsModularLattice (Submodule R M) :=
   ⟨fun x y z xz a ha => by
-    rw [mem_inf, mem_sup] at ha 
+    rw [mem_inf, mem_sup] at ha
     rcases ha with ⟨⟨b, hb, c, hc, rfl⟩, haz⟩
     rw [mem_sup]
     refine' ⟨b, hb, c, mem_inf.2 ⟨hc, _⟩, rfl⟩
@@ -1190,7 +1190,7 @@ theorem ext_on {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (hv : span R s = 
 each `v i`, then they are equal. -/
 theorem ext_on_range {ι : Type _} {v : ι → M} {f g : M →ₛₗ[σ₁₂] M₂} (hv : span R (Set.range v) = ⊤)
     (h : ∀ i, f (v i) = g (v i)) : f = g :=
-  ext_on hv (Set.forall_range_iff.2 h)
+  ext_on hv (Set.forall_mem_range.2 h)
 #align linear_map.ext_on_range LinearMap.ext_on_range
 -/
 

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

@@ -835,8 +835,7 @@ theorem finset_span_isCompactElement (S : Finset M) :
   rw [span_eq_supr_of_singleton_spans]
   simp only [Finset.mem_coe]
   rw [← Finset.sup_eq_iSup]
-  exact
-    CompleteLattice.finset_sup_compact_of_compact S fun x _ => singleton_span_is_compact_element x
+  exact CompleteLattice.isCompactElement_finsetSup S fun x _ => singleton_span_is_compact_element x
 #align submodule.finset_span_is_compact_element Submodule.finset_span_isCompactElement
 -/
 

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

@@ -4,9 +4,9 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Frédéric Dupuis,
   Heather Macbeth
 -/
-import Mathbin.LinearAlgebra.Basic
-import Mathbin.Order.CompactlyGenerated
-import Mathbin.Order.OmegaCompletePartialOrder
+import LinearAlgebra.Basic
+import Order.CompactlyGenerated
+import Order.OmegaCompletePartialOrder
 
 #align_import linear_algebra.span from "leanprover-community/mathlib"@"10878f6bf1dab863445907ab23fbfcefcb5845d0"
 

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

@@ -123,7 +123,7 @@ theorem map_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (
 #align submodule.map_span Submodule.map_span
 -/
 
-alias Submodule.map_span ← _root_.linear_map.map_span
+alias _root_.linear_map.map_span := Submodule.map_span
 #align linear_map.map_span LinearMap.map_span
 
 #print Submodule.map_span_le /-
@@ -135,7 +135,7 @@ theorem map_span_le [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂
 #align submodule.map_span_le Submodule.map_span_le
 -/
 
-alias Submodule.map_span_le ← _root_.linear_map.map_span_le
+alias _root_.linear_map.map_span_le := Submodule.map_span_le
 #align linear_map.map_span_le LinearMap.map_span_le
 
 #print Submodule.span_insert_zero /-
@@ -156,7 +156,7 @@ theorem span_preimage_le (f : M →ₛₗ[σ₁₂] M₂) (s : Set M₂) :
 #align submodule.span_preimage_le Submodule.span_preimage_le
 -/
 
-alias Submodule.span_preimage_le ← _root_.linear_map.span_preimage_le
+alias _root_.linear_map.span_preimage_le := Submodule.span_preimage_le
 #align linear_map.span_preimage_le LinearMap.span_preimage_le
 
 #print Submodule.closure_subset_span /-

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

@@ -917,7 +917,7 @@ theorem mem_span_finite_of_mem_span {S : Set M} {x : M} (hx : x ∈ span R S) :
     · rwa [Finset.coe_singleton, Set.singleton_subset_iff]
     · rw [Finset.coe_singleton]
       exact Submodule.mem_span_singleton_self x
-  · use ∅; simp
+  · use∅; simp
   · rintro x y ⟨X, hX, hxX⟩ ⟨Y, hY, hyY⟩
     refine' ⟨X ∪ Y, _, _⟩
     · rw [Finset.coe_union]

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

@@ -3,16 +3,13 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Frédéric Dupuis,
   Heather Macbeth
-
-! This file was ported from Lean 3 source module linear_algebra.span
-! leanprover-community/mathlib commit 10878f6bf1dab863445907ab23fbfcefcb5845d0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Basic
 import Mathbin.Order.CompactlyGenerated
 import Mathbin.Order.OmegaCompletePartialOrder
 
+#align_import linear_algebra.span from "leanprover-community/mathlib"@"10878f6bf1dab863445907ab23fbfcefcb5845d0"
+
 /-!
 # The span of a set of vectors, as a submodule
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9

@@ -146,7 +146,7 @@ alias Submodule.map_span_le ← _root_.linear_map.map_span_le
 theorem span_insert_zero : span R (insert (0 : M) s) = span R s :=
   by
   refine' le_antisymm _ (Submodule.span_mono (Set.subset_insert 0 s))
-  rw [span_le, Set.insert_subset]
+  rw [span_le, Set.insert_subset_iff]
   exact ⟨by simp only [SetLike.mem_coe, Submodule.zero_mem], Submodule.subset_span⟩
 #align submodule.span_insert_zero Submodule.span_insert_zero
 -/
@@ -627,7 +627,7 @@ theorem span_insert (x) (s : Set M) : span R (insert x s) = span R ({x} : Set M)
 
 #print Submodule.span_insert_eq_span /-
 theorem span_insert_eq_span (h : x ∈ span R s) : span R (insert x s) = span R s :=
-  span_eq_of_le _ (Set.insert_subset.mpr ⟨h, subset_span⟩) (span_mono <| subset_insert _ _)
+  span_eq_of_le _ (Set.insert_subset_iff.mpr ⟨h, subset_span⟩) (span_mono <| subset_insert _ _)
 #align submodule.span_insert_eq_span Submodule.span_insert_eq_span
 -/
 

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

@@ -73,20 +73,28 @@ theorem subset_span : s ⊆ span R s := fun x h => mem_span.2 fun p hp => hp h
 #align submodule.subset_span Submodule.subset_span
 -/
 
+#print Submodule.span_le /-
 theorem span_le {p} : span R s ≤ p ↔ s ⊆ p :=
   ⟨Subset.trans subset_span, fun ss x h => mem_span.1 h _ ss⟩
 #align submodule.span_le Submodule.span_le
+-/
 
+#print Submodule.span_mono /-
 theorem span_mono (h : s ⊆ t) : span R s ≤ span R t :=
   span_le.2 <| Subset.trans h subset_span
 #align submodule.span_mono Submodule.span_mono
+-/
 
+#print Submodule.span_monotone /-
 theorem span_monotone : Monotone (span R : Set M → Submodule R M) := fun _ _ => span_mono
 #align submodule.span_monotone Submodule.span_monotone
+-/
 
+#print Submodule.span_eq_of_le /-
 theorem span_eq_of_le (h₁ : s ⊆ p) (h₂ : p ≤ span R s) : span R s = p :=
   le_antisymm (span_le.2 h₁) h₂
 #align submodule.span_eq_of_le Submodule.span_eq_of_le
+-/
 
 #print Submodule.span_eq /-
 theorem span_eq : span R (p : Set M) = p :=
@@ -100,33 +108,40 @@ theorem span_eq_span (hs : s ⊆ span R t) (ht : t ⊆ span R s) : span R s = sp
 #align submodule.span_eq_span Submodule.span_eq_span
 -/
 
+#print Submodule.span_coe_eq_restrictScalars /-
 /-- A version of `submodule.span_eq` for when the span is by a smaller ring. -/
 @[simp]
 theorem span_coe_eq_restrictScalars [Semiring S] [SMul S R] [Module S M] [IsScalarTower S R M] :
     span S (p : Set M) = p.restrictScalars S :=
   span_eq (p.restrictScalars S)
 #align submodule.span_coe_eq_restrict_scalars Submodule.span_coe_eq_restrictScalars
+-/
 
+#print Submodule.map_span /-
 theorem map_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (s : Set M) :
     (span R s).map f = span R₂ (f '' s) :=
   Eq.symm <|
     span_eq_of_le _ (Set.image_subset f subset_span) <|
       map_le_iff_le_comap.2 <| span_le.2 fun x hx => subset_span ⟨x, hx, rfl⟩
 #align submodule.map_span Submodule.map_span
+-/
 
 alias Submodule.map_span ← _root_.linear_map.map_span
 #align linear_map.map_span LinearMap.map_span
 
+#print Submodule.map_span_le /-
 theorem map_span_le [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (s : Set M) (N : Submodule R₂ M₂) :
     map f (span R s) ≤ N ↔ ∀ m ∈ s, f m ∈ N :=
   by
   rw [f.map_span, span_le, Set.image_subset_iff]
   exact Iff.rfl
 #align submodule.map_span_le Submodule.map_span_le
+-/
 
 alias Submodule.map_span_le ← _root_.linear_map.map_span_le
 #align linear_map.map_span_le LinearMap.map_span_le
 
+#print Submodule.span_insert_zero /-
 @[simp]
 theorem span_insert_zero : span R (insert (0 : M) s) = span R s :=
   by
@@ -134,30 +149,40 @@ theorem span_insert_zero : span R (insert (0 : M) s) = span R s :=
   rw [span_le, Set.insert_subset]
   exact ⟨by simp only [SetLike.mem_coe, Submodule.zero_mem], Submodule.subset_span⟩
 #align submodule.span_insert_zero Submodule.span_insert_zero
+-/
 
+#print Submodule.span_preimage_le /-
 -- See also `span_preimage_eq` below.
 theorem span_preimage_le (f : M →ₛₗ[σ₁₂] M₂) (s : Set M₂) :
     span R (f ⁻¹' s) ≤ (span R₂ s).comap f := by rw [span_le, comap_coe];
   exact preimage_mono subset_span
 #align submodule.span_preimage_le Submodule.span_preimage_le
+-/
 
 alias Submodule.span_preimage_le ← _root_.linear_map.span_preimage_le
 #align linear_map.span_preimage_le LinearMap.span_preimage_le
 
+#print Submodule.closure_subset_span /-
 theorem closure_subset_span {s : Set M} : (AddSubmonoid.closure s : Set M) ⊆ span R s :=
   (@AddSubmonoid.closure_le _ _ _ (span R s).toAddSubmonoid).mpr subset_span
 #align submodule.closure_subset_span Submodule.closure_subset_span
+-/
 
+#print Submodule.closure_le_toAddSubmonoid_span /-
 theorem closure_le_toAddSubmonoid_span {s : Set M} :
     AddSubmonoid.closure s ≤ (span R s).toAddSubmonoid :=
   closure_subset_span
 #align submodule.closure_le_to_add_submonoid_span Submodule.closure_le_toAddSubmonoid_span
+-/
 
+#print Submodule.span_closure /-
 @[simp]
 theorem span_closure {s : Set M} : span R (AddSubmonoid.closure s : Set M) = span R s :=
   le_antisymm (span_le.mpr closure_subset_span) (span_mono AddSubmonoid.subset_closure)
 #align submodule.span_closure Submodule.span_closure
+-/
 
+#print Submodule.span_induction /-
 /-- An induction principle for span membership. If `p` holds for 0 and all elements of `s`, and is
 preserved under addition and scalar multiplication, then `p` holds for all elements of the span of
 `s`. -/
@@ -166,7 +191,9 @@ theorem span_induction {p : M → Prop} (h : x ∈ span R s) (Hs : ∀ x ∈ s,
     (H1 : ∀ x y, p x → p y → p (x + y)) (H2 : ∀ (a : R) (x), p x → p (a • x)) : p x :=
   (@span_le _ _ _ _ _ _ ⟨p, H1, H0, H2⟩).2 Hs h
 #align submodule.span_induction Submodule.span_induction
+-/
 
+#print Submodule.span_induction' /-
 /-- A dependent version of `submodule.span_induction`. -/
 theorem span_induction' {p : ∀ x, x ∈ span R s → Prop} (Hs : ∀ (x) (h : x ∈ s), p x (subset_span h))
     (H0 : p 0 (Submodule.zero_mem _))
@@ -182,7 +209,9 @@ theorem span_induction' {p : ∀ x, x ∈ span R s → Prop} (Hs : ∀ (x) (h :
           Exists.elim hy fun hy' hy => ⟨add_mem hx' hy', H1 _ _ _ _ hx hy⟩)
       fun r x hx => Exists.elim hx fun hx' hx => ⟨smul_mem _ _ hx', H2 r _ _ hx⟩
 #align submodule.span_induction' Submodule.span_induction'
+-/
 
+#print Submodule.span_span_coe_preimage /-
 @[simp]
 theorem span_span_coe_preimage : span R ((coe : span R s → M) ⁻¹' s) = ⊤ :=
   eq_top_iff.2 fun x =>
@@ -194,6 +223,7 @@ theorem span_span_coe_preimage : span R ((coe : span R s → M) ⁻¹' s) = ⊤
       · exact add_mem
       · exact smul_mem _ _
 #align submodule.span_span_coe_preimage Submodule.span_span_coe_preimage
+-/
 
 #print Submodule.span_nat_eq_addSubmonoid_closure /-
 theorem span_nat_eq_addSubmonoid_closure (s : Set M) :
@@ -206,11 +236,14 @@ theorem span_nat_eq_addSubmonoid_closure (s : Set M) :
 #align submodule.span_nat_eq_add_submonoid_closure Submodule.span_nat_eq_addSubmonoid_closure
 -/
 
+#print Submodule.span_nat_eq /-
 @[simp]
 theorem span_nat_eq (s : AddSubmonoid M) : (span ℕ (s : Set M)).toAddSubmonoid = s := by
   rw [span_nat_eq_add_submonoid_closure, s.closure_eq]
 #align submodule.span_nat_eq Submodule.span_nat_eq
+-/
 
+#print Submodule.span_int_eq_addSubgroup_closure /-
 theorem span_int_eq_addSubgroup_closure {M : Type _} [AddCommGroup M] (s : Set M) :
     (span ℤ s).toAddSubgroup = AddSubgroup.closure s :=
   Eq.symm <|
@@ -218,16 +251,20 @@ theorem span_int_eq_addSubgroup_closure {M : Type _} [AddCommGroup M] (s : Set M
       span_induction hx (fun x hx => AddSubgroup.subset_closure hx) (AddSubgroup.zero_mem _)
         (fun _ _ => AddSubgroup.add_mem _) fun _ _ _ => AddSubgroup.zsmul_mem _ ‹_› _
 #align submodule.span_int_eq_add_subgroup_closure Submodule.span_int_eq_addSubgroup_closure
+-/
 
+#print Submodule.span_int_eq /-
 @[simp]
 theorem span_int_eq {M : Type _} [AddCommGroup M] (s : AddSubgroup M) :
     (span ℤ (s : Set M)).toAddSubgroup = s := by rw [span_int_eq_add_subgroup_closure, s.closure_eq]
 #align submodule.span_int_eq Submodule.span_int_eq
+-/
 
 section
 
 variable (R M)
 
+#print Submodule.gi /-
 /-- `span` forms a Galois insertion with the coercion from submodule to set. -/
 protected def gi : GaloisInsertion (@span R M _ _ _) coe
     where
@@ -236,64 +273,86 @@ protected def gi : GaloisInsertion (@span R M _ _ _) coe
   le_l_u s := subset_span
   choice_eq s h := rfl
 #align submodule.gi Submodule.gi
+-/
 
 end
 
+#print Submodule.span_empty /-
 @[simp]
 theorem span_empty : span R (∅ : Set M) = ⊥ :=
   (Submodule.gi R M).gc.l_bot
 #align submodule.span_empty Submodule.span_empty
+-/
 
+#print Submodule.span_univ /-
 @[simp]
 theorem span_univ : span R (univ : Set M) = ⊤ :=
   eq_top_iff.2 <| SetLike.le_def.2 <| subset_span
 #align submodule.span_univ Submodule.span_univ
+-/
 
+#print Submodule.span_union /-
 theorem span_union (s t : Set M) : span R (s ∪ t) = span R s ⊔ span R t :=
   (Submodule.gi R M).gc.l_sup
 #align submodule.span_union Submodule.span_union
+-/
 
+#print Submodule.span_iUnion /-
 theorem span_iUnion {ι} (s : ι → Set M) : span R (⋃ i, s i) = ⨆ i, span R (s i) :=
   (Submodule.gi R M).gc.l_iSup
 #align submodule.span_Union Submodule.span_iUnion
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print Submodule.span_iUnion₂ /-
 theorem span_iUnion₂ {ι} {κ : ι → Sort _} (s : ∀ i, κ i → Set M) :
     span R (⋃ (i) (j), s i j) = ⨆ (i) (j), span R (s i j) :=
   (Submodule.gi R M).gc.l_iSup₂
 #align submodule.span_Union₂ Submodule.span_iUnion₂
+-/
 
+#print Submodule.span_attach_biUnion /-
 theorem span_attach_biUnion [DecidableEq M] {α : Type _} (s : Finset α) (f : s → Finset M) :
     span R (s.attach.biUnion f : Set M) = ⨆ x, span R (f x) := by simpa [span_Union]
 #align submodule.span_attach_bUnion Submodule.span_attach_biUnion
+-/
 
+#print Submodule.sup_span /-
 theorem sup_span : p ⊔ span R s = span R (p ∪ s) := by rw [Submodule.span_union, p.span_eq]
 #align submodule.sup_span Submodule.sup_span
+-/
 
+#print Submodule.span_sup /-
 theorem span_sup : span R s ⊔ p = span R (s ∪ p) := by rw [Submodule.span_union, p.span_eq]
 #align submodule.span_sup Submodule.span_sup
+-/
 
--- mathport name: «expr ∙ »
 notation:1000
   /- Note that the character `∙` U+2219 used below is different from the scalar multiplication
 character `•` U+2022 and the matrix multiplication character `⬝` U+2B1D. -/
 R " ∙ " x => span R (@singleton _ _ Set.hasSingleton x)
 
+#print Submodule.span_eq_iSup_of_singleton_spans /-
 theorem span_eq_iSup_of_singleton_spans (s : Set M) : span R s = ⨆ x ∈ s, R ∙ x := by
   simp only [← span_Union, Set.biUnion_of_singleton s]
 #align submodule.span_eq_supr_of_singleton_spans Submodule.span_eq_iSup_of_singleton_spans
+-/
 
+#print Submodule.span_range_eq_iSup /-
 theorem span_range_eq_iSup {ι : Type _} {v : ι → M} : span R (range v) = ⨆ i, R ∙ v i := by
   rw [span_eq_supr_of_singleton_spans, iSup_range]
 #align submodule.span_range_eq_supr Submodule.span_range_eq_iSup
+-/
 
+#print Submodule.span_smul_le /-
 theorem span_smul_le (s : Set M) (r : R) : span R (r • s) ≤ span R s :=
   by
   rw [span_le]
   rintro _ ⟨x, hx, rfl⟩
   exact smul_mem (span R s) r (subset_span hx)
 #align submodule.span_smul_le Submodule.span_smul_le
+-/
 
 #print Submodule.subset_span_trans /-
 theorem subset_span_trans {U V W : Set M} (hUV : U ⊆ Submodule.span R V)
@@ -316,6 +375,7 @@ theorem span_smul_eq_of_isUnit (s : Set M) (r : R) (hr : IsUnit r) : span R (r 
 #align submodule.span_smul_eq_of_is_unit Submodule.span_smul_eq_of_isUnit
 -/
 
+#print Submodule.coe_iSup_of_directed /-
 @[simp]
 theorem coe_iSup_of_directed {ι} [hι : Nonempty ι] (S : ι → Submodule R M)
     (H : Directed (· ≤ ·) S) : ((iSup S : Submodule R M) : Set M) = ⋃ i, S i :=
@@ -330,40 +390,52 @@ theorem coe_iSup_of_directed {ι} [hι : Nonempty ι] (S : ι → Submodule R M)
     exact ⟨k, add_mem (ik hi) (jk hj)⟩
   · exact fun a x i hi => ⟨i, smul_mem _ a hi⟩
 #align submodule.coe_supr_of_directed Submodule.coe_iSup_of_directed
+-/
 
+#print Submodule.mem_iSup_of_directed /-
 @[simp]
 theorem mem_iSup_of_directed {ι} [Nonempty ι] (S : ι → Submodule R M) (H : Directed (· ≤ ·) S) {x} :
     x ∈ iSup S ↔ ∃ i, x ∈ S i := by rw [← SetLike.mem_coe, coe_supr_of_directed S H, mem_Union]; rfl
 #align submodule.mem_supr_of_directed Submodule.mem_iSup_of_directed
+-/
 
+#print Submodule.mem_sSup_of_directed /-
 theorem mem_sSup_of_directed {s : Set (Submodule R M)} {z} (hs : s.Nonempty)
     (hdir : DirectedOn (· ≤ ·) s) : z ∈ sSup s ↔ ∃ y ∈ s, z ∈ y :=
   by
   haveI : Nonempty s := hs.to_subtype
   simp only [sSup_eq_iSup', mem_supr_of_directed _ hdir.directed_coe, SetCoe.exists, Subtype.coe_mk]
 #align submodule.mem_Sup_of_directed Submodule.mem_sSup_of_directed
+-/
 
+#print Submodule.coe_iSup_of_chain /-
 @[norm_cast, simp]
 theorem coe_iSup_of_chain (a : ℕ →o Submodule R M) : (↑(⨆ k, a k) : Set M) = ⋃ k, (a k : Set M) :=
   coe_iSup_of_directed a a.Monotone.directed_le
 #align submodule.coe_supr_of_chain Submodule.coe_iSup_of_chain
+-/
 
+#print Submodule.coe_scott_continuous /-
 /-- We can regard `coe_supr_of_chain` as the statement that `coe : (submodule R M) → set M` is
 Scott continuous for the ω-complete partial order induced by the complete lattice structures. -/
 theorem coe_scott_continuous :
     OmegaCompletePartialOrder.Continuous' (coe : Submodule R M → Set M) :=
   ⟨SetLike.coe_mono, coe_iSup_of_chain⟩
 #align submodule.coe_scott_continuous Submodule.coe_scott_continuous
+-/
 
+#print Submodule.mem_iSup_of_chain /-
 @[simp]
 theorem mem_iSup_of_chain (a : ℕ →o Submodule R M) (m : M) : (m ∈ ⨆ k, a k) ↔ ∃ k, m ∈ a k :=
   mem_iSup_of_directed a a.Monotone.directed_le
 #align submodule.mem_supr_of_chain Submodule.mem_iSup_of_chain
+-/
 
 section
 
 variable {p p'}
 
+#print Submodule.mem_sup /-
 theorem mem_sup : x ∈ p ⊔ p' ↔ ∃ y ∈ p, ∃ z ∈ p', y + z = x :=
   ⟨fun h => by
     rw [← span_eq p, ← span_eq p', ← span_union] at h 
@@ -379,24 +451,32 @@ theorem mem_sup : x ∈ p ⊔ p' ↔ ∃ y ∈ p, ∃ z ∈ p', y + z = x :=
     rintro ⟨y, hy, z, hz, rfl⟩ <;>
       exact add_mem ((le_sup_left : p ≤ p ⊔ p') hy) ((le_sup_right : p' ≤ p ⊔ p') hz)⟩
 #align submodule.mem_sup Submodule.mem_sup
+-/
 
+#print Submodule.mem_sup' /-
 theorem mem_sup' : x ∈ p ⊔ p' ↔ ∃ (y : p) (z : p'), (y : M) + z = x :=
   mem_sup.trans <| by simp only [SetLike.exists, coe_mk]
 #align submodule.mem_sup' Submodule.mem_sup'
+-/
 
 variable (p p')
 
+#print Submodule.coe_sup /-
 theorem coe_sup : ↑(p ⊔ p') = (p + p' : Set M) := by ext;
   rw [SetLike.mem_coe, mem_sup, Set.mem_add]; simp
 #align submodule.coe_sup Submodule.coe_sup
+-/
 
+#print Submodule.sup_toAddSubmonoid /-
 theorem sup_toAddSubmonoid : (p ⊔ p').toAddSubmonoid = p.toAddSubmonoid ⊔ p'.toAddSubmonoid :=
   by
   ext x
   rw [mem_to_add_submonoid, mem_sup, AddSubmonoid.mem_sup]
   rfl
 #align submodule.sup_to_add_submonoid Submodule.sup_toAddSubmonoid
+-/
 
+#print Submodule.sup_toAddSubgroup /-
 theorem sup_toAddSubgroup {R M : Type _} [Ring R] [AddCommGroup M] [Module R M]
     (p p' : Submodule R M) : (p ⊔ p').toAddSubgroup = p.toAddSubgroup ⊔ p'.toAddSubgroup :=
   by
@@ -404,6 +484,7 @@ theorem sup_toAddSubgroup {R M : Type _} [Ring R] [AddCommGroup M] [Module R M]
   rw [mem_to_add_subgroup, mem_sup, AddSubgroup.mem_sup]
   rfl
 #align submodule.sup_to_add_subgroup Submodule.sup_toAddSubgroup
+-/
 
 end
 
@@ -413,6 +494,7 @@ theorem mem_span_singleton_self (x : M) : x ∈ R ∙ x :=
 #align submodule.mem_span_singleton_self Submodule.mem_span_singleton_self
 -/
 
+#print Submodule.nontrivial_span_singleton /-
 theorem nontrivial_span_singleton {x : M} (h : x ≠ 0) : Nontrivial (R ∙ x) :=
   ⟨by
     use 0, x, Submodule.mem_span_singleton_self x
@@ -420,6 +502,7 @@ theorem nontrivial_span_singleton {x : M} (h : x ≠ 0) : Nontrivial (R ∙ x) :
     rw [eq_comm, Submodule.mk_eq_zero] at H 
     exact h H⟩
 #align submodule.nontrivial_span_singleton Submodule.nontrivial_span_singleton
+-/
 
 #print Submodule.mem_span_singleton /-
 theorem mem_span_singleton {y : M} : (x ∈ R ∙ y) ↔ ∃ a : R, a • y = x :=
@@ -435,19 +518,25 @@ theorem mem_span_singleton {y : M} : (x ∈ R ∙ y) ↔ ∃ a : R, a • y = x
 #align submodule.mem_span_singleton Submodule.mem_span_singleton
 -/
 
+#print Submodule.le_span_singleton_iff /-
 theorem le_span_singleton_iff {s : Submodule R M} {v₀ : M} :
     (s ≤ R ∙ v₀) ↔ ∀ v ∈ s, ∃ r : R, r • v₀ = v := by simp_rw [SetLike.le_def, mem_span_singleton]
 #align submodule.le_span_singleton_iff Submodule.le_span_singleton_iff
+-/
 
 variable (R)
 
+#print Submodule.span_singleton_eq_top_iff /-
 theorem span_singleton_eq_top_iff (x : M) : (R ∙ x) = ⊤ ↔ ∀ v, ∃ r : R, r • x = v := by
   rw [eq_top_iff, le_span_singleton_iff]; tauto
 #align submodule.span_singleton_eq_top_iff Submodule.span_singleton_eq_top_iff
+-/
 
+#print Submodule.span_zero_singleton /-
 @[simp]
 theorem span_zero_singleton : (R ∙ (0 : M)) = ⊥ := by ext; simp [mem_span_singleton, eq_comm]
 #align submodule.span_zero_singleton Submodule.span_zero_singleton
+-/
 
 #print Submodule.span_singleton_eq_range /-
 theorem span_singleton_eq_range (y : M) : ↑(R ∙ y) = range ((· • y) : R → M) :=
@@ -455,13 +544,16 @@ theorem span_singleton_eq_range (y : M) : ↑(R ∙ y) = range ((· • y) : R 
 #align submodule.span_singleton_eq_range Submodule.span_singleton_eq_range
 -/
 
+#print Submodule.span_singleton_smul_le /-
 theorem span_singleton_smul_le {S} [Monoid S] [SMul S R] [MulAction S M] [IsScalarTower S R M]
     (r : S) (x : M) : (R ∙ r • x) ≤ R ∙ x :=
   by
   rw [span_le, Set.singleton_subset_iff, SetLike.mem_coe]
   exact smul_of_tower_mem _ _ (mem_span_singleton_self _)
 #align submodule.span_singleton_smul_le Submodule.span_singleton_smul_le
+-/
 
+#print Submodule.span_singleton_group_smul_eq /-
 theorem span_singleton_group_smul_eq {G} [Group G] [SMul G R] [MulAction G M] [IsScalarTower G R M]
     (g : G) (x : M) : (R ∙ g • x) = R ∙ x :=
   by
@@ -469,16 +561,20 @@ theorem span_singleton_group_smul_eq {G} [Group G] [SMul G R] [MulAction G M] [I
   convert span_singleton_smul_le R g⁻¹ (g • x)
   exact (inv_smul_smul g x).symm
 #align submodule.span_singleton_group_smul_eq Submodule.span_singleton_group_smul_eq
+-/
 
 variable {R}
 
+#print Submodule.span_singleton_smul_eq /-
 theorem span_singleton_smul_eq {r : R} (hr : IsUnit r) (x : M) : (R ∙ r • x) = R ∙ x :=
   by
   lift r to Rˣ using hr
   rw [← Units.smul_def]
   exact span_singleton_group_smul_eq R r x
 #align submodule.span_singleton_smul_eq Submodule.span_singleton_smul_eq
+-/
 
+#print Submodule.disjoint_span_singleton /-
 theorem disjoint_span_singleton {K E : Type _} [DivisionRing K] [AddCommGroup E] [Module K E]
     {s : Submodule K E} {x : E} : Disjoint s (K ∙ x) ↔ x ∈ s → x = 0 :=
   by
@@ -490,11 +586,14 @@ theorem disjoint_span_singleton {K E : Type _} [DivisionRing K] [AddCommGroup E]
   · rw [s.smul_mem_iff hc] at hy 
     rw [H hy, smul_zero]
 #align submodule.disjoint_span_singleton Submodule.disjoint_span_singleton
+-/
 
+#print Submodule.disjoint_span_singleton' /-
 theorem disjoint_span_singleton' {K E : Type _} [DivisionRing K] [AddCommGroup E] [Module K E]
     {p : Submodule K E} {x : E} (x0 : x ≠ 0) : Disjoint p (K ∙ x) ↔ x ∉ p :=
   disjoint_span_singleton.trans ⟨fun h₁ h₂ => x0 (h₁ h₂), fun h₁ h₂ => (h₁ h₂).elim⟩
 #align submodule.disjoint_span_singleton' Submodule.disjoint_span_singleton'
+-/
 
 #print Submodule.mem_span_singleton_trans /-
 theorem mem_span_singleton_trans {x y z : M} (hxy : x ∈ R ∙ y) (hyz : y ∈ R ∙ z) : x ∈ R ∙ z :=
@@ -504,6 +603,7 @@ theorem mem_span_singleton_trans {x y z : M} (hxy : x ∈ R ∙ y) (hyz : y ∈
 #align submodule.mem_span_singleton_trans Submodule.mem_span_singleton_trans
 -/
 
+#print Submodule.mem_span_insert /-
 theorem mem_span_insert {y} : x ∈ span R (insert y s) ↔ ∃ a : R, ∃ z ∈ span R s, x = a • y + z :=
   by
   simp only [← union_singleton, span_union, mem_sup, mem_span_singleton, exists_prop,
@@ -511,14 +611,19 @@ theorem mem_span_insert {y} : x ∈ span R (insert y s) ↔ ∃ a : R, ∃ z ∈
   rw [exists_comm]
   simp only [eq_comm, add_comm, exists_and_left]
 #align submodule.mem_span_insert Submodule.mem_span_insert
+-/
 
+#print Submodule.mem_span_pair /-
 theorem mem_span_pair {x y z : M} : z ∈ span R ({x, y} : Set M) ↔ ∃ a b : R, a • x + b • y = z := by
   simp_rw [mem_span_insert, mem_span_singleton, exists_prop, exists_exists_eq_and, eq_comm]
 #align submodule.mem_span_pair Submodule.mem_span_pair
+-/
 
+#print Submodule.span_insert /-
 theorem span_insert (x) (s : Set M) : span R (insert x s) = span R ({x} : Set M) ⊔ span R s := by
   rw [insert_eq, span_union]
 #align submodule.span_insert Submodule.span_insert
+-/
 
 #print Submodule.span_insert_eq_span /-
 theorem span_insert_eq_span (h : x ∈ span R s) : span R (insert x s) = span R s :=
@@ -534,43 +639,56 @@ theorem span_span : span R (span R s : Set M) = span R s :=
 
 variable (R S s)
 
+#print Submodule.span_le_restrictScalars /-
 /-- If `R` is "smaller" ring than `S` then the span by `R` is smaller than the span by `S`. -/
 theorem span_le_restrictScalars [Semiring S] [SMul R S] [Module S M] [IsScalarTower R S M] :
     span R s ≤ (span S s).restrictScalars R :=
   Submodule.span_le.2 Submodule.subset_span
 #align submodule.span_le_restrict_scalars Submodule.span_le_restrictScalars
+-/
 
+#print Submodule.span_subset_span /-
 /-- A version of `submodule.span_le_restrict_scalars` with coercions. -/
 @[simp]
 theorem span_subset_span [Semiring S] [SMul R S] [Module S M] [IsScalarTower R S M] :
     ↑(span R s) ⊆ (span S s : Set M) :=
   span_le_restrictScalars R S s
 #align submodule.span_subset_span Submodule.span_subset_span
+-/
 
+#print Submodule.span_span_of_tower /-
 /-- Taking the span by a large ring of the span by the small ring is the same as taking the span
 by just the large ring. -/
 theorem span_span_of_tower [Semiring S] [SMul R S] [Module S M] [IsScalarTower R S M] :
     span S (span R s : Set M) = span S s :=
   le_antisymm (span_le.2 <| span_subset_span R S s) (span_mono subset_span)
 #align submodule.span_span_of_tower Submodule.span_span_of_tower
+-/
 
 variable {R S s}
 
+#print Submodule.span_eq_bot /-
 theorem span_eq_bot : span R (s : Set M) = ⊥ ↔ ∀ x ∈ s, (x : M) = 0 :=
   eq_bot_iff.trans
     ⟨fun H x h => (mem_bot R).1 <| H <| subset_span h, fun H =>
       span_le.2 fun x h => (mem_bot R).2 <| H x h⟩
 #align submodule.span_eq_bot Submodule.span_eq_bot
+-/
 
+#print Submodule.span_singleton_eq_bot /-
 @[simp]
 theorem span_singleton_eq_bot : (R ∙ x) = ⊥ ↔ x = 0 :=
   span_eq_bot.trans <| by simp
 #align submodule.span_singleton_eq_bot Submodule.span_singleton_eq_bot
+-/
 
+#print Submodule.span_zero /-
 @[simp]
 theorem span_zero : span R (0 : Set M) = ⊥ := by rw [← singleton_zero, span_singleton_eq_bot]
 #align submodule.span_zero Submodule.span_zero
+-/
 
+#print Submodule.span_singleton_eq_span_singleton /-
 theorem span_singleton_eq_span_singleton {R M : Type _} [Ring R] [AddCommGroup M] [Module R M]
     [NoZeroSMulDivisors R M] {x y : M} : ((R ∙ x) = R ∙ y) ↔ ∃ z : Rˣ, z • x = y :=
   by
@@ -592,40 +710,54 @@ theorem span_singleton_eq_span_singleton {R M : Type _} [Ring R] [AddCommGroup M
   · rintro ⟨v, rfl⟩
     rw [span_singleton_group_smul_eq]
 #align submodule.span_singleton_eq_span_singleton Submodule.span_singleton_eq_span_singleton
+-/
 
+#print Submodule.span_image /-
 @[simp]
 theorem span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) :
     span R₂ (f '' s) = map f (span R s) :=
   (map_span f s).symm
 #align submodule.span_image Submodule.span_image
+-/
 
+#print Submodule.apply_mem_span_image_of_mem_span /-
 theorem apply_mem_span_image_of_mem_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) {x : M}
     {s : Set M} (h : x ∈ Submodule.span R s) : f x ∈ Submodule.span R₂ (f '' s) :=
   by
   rw [Submodule.span_image]
   exact Submodule.mem_map_of_mem h
 #align submodule.apply_mem_span_image_of_mem_span Submodule.apply_mem_span_image_of_mem_span
+-/
 
+#print Submodule.map_subtype_span_singleton /-
 @[simp]
 theorem map_subtype_span_singleton {p : Submodule R M} (x : p) :
     map p.Subtype (R ∙ x) = R ∙ (x : M) := by simp [← span_image]
 #align submodule.map_subtype_span_singleton Submodule.map_subtype_span_singleton
+-/
 
+#print Submodule.not_mem_span_of_apply_not_mem_span_image /-
 /-- `f` is an explicit argument so we can `apply` this theorem and obtain `h` as a new goal. -/
 theorem not_mem_span_of_apply_not_mem_span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) {x : M}
     {s : Set M} (h : f x ∉ Submodule.span R₂ (f '' s)) : x ∉ Submodule.span R s :=
   h.imp (apply_mem_span_image_of_mem_span f)
 #align submodule.not_mem_span_of_apply_not_mem_span_image Submodule.not_mem_span_of_apply_not_mem_span_image
+-/
 
+#print Submodule.iSup_span /-
 theorem iSup_span {ι : Sort _} (p : ι → Set M) : (⨆ i, span R (p i)) = span R (⋃ i, p i) :=
   le_antisymm (iSup_le fun i => span_mono <| subset_iUnion _ i) <|
     span_le.mpr <| iUnion_subset fun i m hm => mem_iSup_of_mem i <| subset_span hm
 #align submodule.supr_span Submodule.iSup_span
+-/
 
+#print Submodule.iSup_eq_span /-
 theorem iSup_eq_span {ι : Sort _} (p : ι → Submodule R M) : (⨆ i, p i) = span R (⋃ i, ↑(p i)) := by
   simp_rw [← supr_span, span_eq]
 #align submodule.supr_eq_span Submodule.iSup_eq_span
+-/
 
+#print Submodule.iSup_toAddSubmonoid /-
 theorem iSup_toAddSubmonoid {ι : Sort _} (p : ι → Submodule R M) :
     (⨆ i, p i).toAddSubmonoid = ⨆ i, (p i).toAddSubmonoid :=
   by
@@ -646,7 +778,9 @@ theorem iSup_toAddSubmonoid {ι : Sort _} (p : ι → Submodule R M) :
       rw [smul_add]
       exact AddSubmonoid.add_mem _ hx hy
 #align submodule.supr_to_add_submonoid Submodule.iSup_toAddSubmonoid
+-/
 
+#print Submodule.iSup_induction /-
 /-- An induction principle for elements of `⨆ i, p i`.
 If `C` holds for `0` and all elements of `p i` for all `i`, and is preserved under addition,
 then it holds for all elements of the supremum of `p`. -/
@@ -658,7 +792,9 @@ theorem iSup_induction {ι : Sort _} (p : ι → Submodule R M) {C : M → Prop}
   rw [← mem_to_add_submonoid, supr_to_add_submonoid] at hx 
   exact AddSubmonoid.iSup_induction _ hx hp h0 hadd
 #align submodule.supr_induction Submodule.iSup_induction
+-/
 
+#print Submodule.iSup_induction' /-
 /-- A dependent version of `submodule.supr_induction`. -/
 @[elab_as_elim]
 theorem iSup_induction' {ι : Sort _} (p : ι → Submodule R M) {C : ∀ x, (x ∈ ⨆ i, p i) → Prop}
@@ -673,11 +809,14 @@ theorem iSup_induction' {ι : Sort _} (p : ι → Submodule R M) {C : ∀ x, (x
   · rintro ⟨_, Cx⟩ ⟨_, Cy⟩
     refine' ⟨_, hadd _ _ _ _ Cx Cy⟩
 #align submodule.supr_induction' Submodule.iSup_induction'
+-/
 
+#print Submodule.span_singleton_le_iff_mem /-
 @[simp]
 theorem span_singleton_le_iff_mem (m : M) (p : Submodule R M) : (R ∙ m) ≤ p ↔ m ∈ p := by
   rw [span_le, singleton_subset_iff, SetLike.mem_coe]
 #align submodule.span_singleton_le_iff_mem Submodule.span_singleton_le_iff_mem
+-/
 
 #print Submodule.singleton_span_isCompactElement /-
 theorem singleton_span_isCompactElement (x : M) :
@@ -720,6 +859,7 @@ instance : IsCompactlyGenerated (Submodule R M) :=
         apply singleton_span_is_compact_element, by
         rw [sSup_eq_iSup, iSup_image, ← span_eq_supr_of_singleton_spans, span_eq]⟩⟩⟩
 
+#print Submodule.submodule_eq_sSup_le_nonzero_spans /-
 /-- A submodule is equal to the supremum of the spans of the submodule's nonzero elements. -/
 theorem submodule_eq_sSup_le_nonzero_spans (p : Submodule R M) :
     p = sSup {T : Submodule R M | ∃ (m : M) (hm : m ∈ p) (hz : m ≠ 0), T = span R {m}} :=
@@ -731,7 +871,9 @@ theorem submodule_eq_sSup_le_nonzero_spans (p : Submodule R M) :
     · exact @le_sSup _ _ S _ ⟨m, ⟨hm, ⟨h, rfl⟩⟩⟩ m (mem_span_singleton_self m)
   · rw [sSup_le_iff]; rintro S ⟨_, ⟨_, ⟨_, rfl⟩⟩⟩; rwa [span_singleton_le_iff_mem]
 #align submodule.submodule_eq_Sup_le_nonzero_spans Submodule.submodule_eq_sSup_le_nonzero_spans
+-/
 
+#print Submodule.lt_sup_iff_not_mem /-
 theorem lt_sup_iff_not_mem {I : Submodule R M} {a : M} : (I < I ⊔ R ∙ a) ↔ a ∉ I :=
   by
   constructor
@@ -752,13 +894,16 @@ theorem lt_sup_iff_not_mem {I : Submodule R M} {a : M} : (I < I ⊔ R ∙ a) ↔
     · have : (R ∙ a) ≤ I ⊔ R ∙ a := le_sup_right
       exact this (mem_span_singleton_self a)
 #align submodule.lt_sup_iff_not_mem Submodule.lt_sup_iff_not_mem
+-/
 
+#print Submodule.mem_iSup /-
 theorem mem_iSup {ι : Sort _} (p : ι → Submodule R M) {m : M} :
     (m ∈ ⨆ i, p i) ↔ ∀ N, (∀ i, p i ≤ N) → m ∈ N :=
   by
   rw [← span_singleton_le_iff_mem, le_iSup_iff]
   simp only [span_singleton_le_iff_mem]
 #align submodule.mem_supr Submodule.mem_iSup
+-/
 
 section
 
@@ -792,6 +937,7 @@ end
 variable {M' : Type _} [AddCommMonoid M'] [Module R M'] (q₁ q₁' : Submodule R M')
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Submodule.prod /-
 /-- The product of two submodules is a submodule. -/
 def prod : Submodule R (M × M') :=
   {
@@ -799,42 +945,58 @@ def prod : Submodule R (M × M') :=
     carrier := p ×ˢ q₁
     smul_mem' := by rintro a ⟨x, y⟩ ⟨hx, hy⟩ <;> exact ⟨smul_mem _ a hx, smul_mem _ a hy⟩ }
 #align submodule.prod Submodule.prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Submodule.prod_coe /-
 @[simp]
 theorem prod_coe : (prod p q₁ : Set (M × M')) = p ×ˢ q₁ :=
   rfl
 #align submodule.prod_coe Submodule.prod_coe
+-/
 
+#print Submodule.mem_prod /-
 @[simp]
 theorem mem_prod {p : Submodule R M} {q : Submodule R M'} {x : M × M'} :
     x ∈ prod p q ↔ x.1 ∈ p ∧ x.2 ∈ q :=
   Set.mem_prod
 #align submodule.mem_prod Submodule.mem_prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Submodule.span_prod_le /-
 theorem span_prod_le (s : Set M) (t : Set M') : span R (s ×ˢ t) ≤ prod (span R s) (span R t) :=
   span_le.2 <| Set.prod_mono subset_span subset_span
 #align submodule.span_prod_le Submodule.span_prod_le
+-/
 
+#print Submodule.prod_top /-
 @[simp]
 theorem prod_top : (prod ⊤ ⊤ : Submodule R (M × M')) = ⊤ := by ext <;> simp
 #align submodule.prod_top Submodule.prod_top
+-/
 
+#print Submodule.prod_bot /-
 @[simp]
 theorem prod_bot : (prod ⊥ ⊥ : Submodule R (M × M')) = ⊥ := by ext ⟨x, y⟩ <;> simp [Prod.zero_eq_mk]
 #align submodule.prod_bot Submodule.prod_bot
+-/
 
+#print Submodule.prod_mono /-
 theorem prod_mono {p p' : Submodule R M} {q q' : Submodule R M'} :
     p ≤ p' → q ≤ q' → prod p q ≤ prod p' q' :=
   prod_mono
 #align submodule.prod_mono Submodule.prod_mono
+-/
 
+#print Submodule.prod_inf_prod /-
 @[simp]
 theorem prod_inf_prod : prod p q₁ ⊓ prod p' q₁' = prod (p ⊓ p') (q₁ ⊓ q₁') :=
   SetLike.coe_injective Set.prod_inter_prod
 #align submodule.prod_inf_prod Submodule.prod_inf_prod
+-/
 
+#print Submodule.prod_sup_prod /-
 @[simp]
 theorem prod_sup_prod : prod p q₁ ⊔ prod p' q₁' = prod (p ⊔ p') (q₁ ⊔ q₁') :=
   by
@@ -845,6 +1007,7 @@ theorem prod_sup_prod : prod p q₁ ⊔ prod p' q₁' = prod (p ⊔ p') (q₁ 
   rcases mem_sup.1 hyy with ⟨y, hy, y', hy', rfl⟩
   refine' mem_sup.2 ⟨(x, y), ⟨hx, hy⟩, (x', y'), ⟨hx', hy'⟩, rfl⟩
 #align submodule.prod_sup_prod Submodule.prod_sup_prod
+-/
 
 end AddCommMonoid
 
@@ -852,6 +1015,7 @@ section AddCommGroup
 
 variable [Ring R] [AddCommGroup M] [Module R M]
 
+#print Submodule.span_neg /-
 @[simp]
 theorem span_neg (s : Set M) : span R (-s) = span R s :=
   calc
@@ -859,7 +1023,9 @@ theorem span_neg (s : Set M) : span R (-s) = span R s :=
     _ = map (-LinearMap.id) (span R s) := ((-LinearMap.id).map_span _).symm
     _ = span R s := by simp
 #align submodule.span_neg Submodule.span_neg
+-/
 
+#print Submodule.mem_span_insert' /-
 theorem mem_span_insert' {x y} {s : Set M} :
     x ∈ span R (insert y s) ↔ ∃ a : R, x + a • y ∈ span R s :=
   by
@@ -867,6 +1033,7 @@ theorem mem_span_insert' {x y} {s : Set M} :
   · rintro ⟨a, z, hz, rfl⟩; exact ⟨-a, by simp [hz, add_assoc]⟩
   · rintro ⟨a, h⟩; exact ⟨-a, _, h, by simp [add_comm, add_left_comm]⟩
 #align submodule.mem_span_insert' Submodule.mem_span_insert'
+-/
 
 instance : IsModularLattice (Submodule R M) :=
   ⟨fun x y z xz a ha => by
@@ -889,20 +1056,20 @@ variable {τ₁₂ : R →+* R₂} [RingHomSurjective τ₁₂]
 
 variable {F : Type _} [sc : SemilinearMapClass F τ₁₂ M M₂]
 
-include sc
-
+#print Submodule.comap_map_eq /-
 theorem comap_map_eq (f : F) (p : Submodule R M) : comap f (map f p) = p ⊔ LinearMap.ker f :=
   by
   refine' le_antisymm _ (sup_le (le_comap_map _ _) (comap_mono bot_le))
   rintro x ⟨y, hy, e⟩
   exact mem_sup.2 ⟨y, hy, x - y, by simpa using sub_eq_zero.2 e.symm, by simp⟩
 #align submodule.comap_map_eq Submodule.comap_map_eq
+-/
 
+#print Submodule.comap_map_eq_self /-
 theorem comap_map_eq_self {f : F} {p : Submodule R M} (h : LinearMap.ker f ≤ p) :
     comap f (map f p) = p := by rw [Submodule.comap_map_eq, sup_of_le_left h]
 #align submodule.comap_map_eq_self Submodule.comap_map_eq_self
-
-omit sc
+-/
 
 end AddCommGroup
 
@@ -924,26 +1091,30 @@ variable {τ₁₂ : R →+* R₂} [RingHomSurjective τ₁₂]
 
 variable {F : Type _} [sc : SemilinearMapClass F τ₁₂ M M₂]
 
-include R
-
-include sc
-
+#print LinearMap.map_le_map_iff /-
 protected theorem map_le_map_iff (f : F) {p p'} : map f p ≤ map f p' ↔ p ≤ p' ⊔ ker f := by
   rw [map_le_iff_le_comap, Submodule.comap_map_eq]
 #align linear_map.map_le_map_iff LinearMap.map_le_map_iff
+-/
 
+#print LinearMap.map_le_map_iff' /-
 theorem map_le_map_iff' {f : F} (hf : ker f = ⊥) {p p'} : map f p ≤ map f p' ↔ p ≤ p' := by
   rw [LinearMap.map_le_map_iff, hf, sup_bot_eq]
 #align linear_map.map_le_map_iff' LinearMap.map_le_map_iff'
+-/
 
+#print LinearMap.map_injective /-
 theorem map_injective {f : F} (hf : ker f = ⊥) : Injective (map f) := fun p p' h =>
   le_antisymm ((map_le_map_iff' hf).1 (le_of_eq h)) ((map_le_map_iff' hf).1 (ge_of_eq h))
 #align linear_map.map_injective LinearMap.map_injective
+-/
 
+#print LinearMap.map_eq_top_iff /-
 theorem map_eq_top_iff {f : F} (hf : range f = ⊤) {p : Submodule R M} :
     p.map f = ⊤ ↔ p ⊔ LinearMap.ker f = ⊤ := by
   simp_rw [← top_le_iff, ← hf, range_eq_map, LinearMap.map_le_map_iff]
 #align linear_map.map_eq_top_iff LinearMap.map_eq_top_iff
+-/
 
 end AddCommGroup
 
@@ -967,14 +1138,18 @@ theorem span_singleton_eq_range (x : M) : (R ∙ x) = (toSpanSingleton R M x).ra
 #align linear_map.span_singleton_eq_range LinearMap.span_singleton_eq_range
 -/
 
+#print LinearMap.toSpanSingleton_one /-
 @[simp]
 theorem toSpanSingleton_one (x : M) : toSpanSingleton R M x 1 = x :=
   one_smul _ _
 #align linear_map.to_span_singleton_one LinearMap.toSpanSingleton_one
+-/
 
+#print LinearMap.toSpanSingleton_zero /-
 @[simp]
 theorem toSpanSingleton_zero : toSpanSingleton R M 0 = 0 := by ext; simp
 #align linear_map.to_span_singleton_zero LinearMap.toSpanSingleton_zero
+-/
 
 end
 
@@ -986,13 +1161,16 @@ variable [Semiring R₂] [AddCommMonoid M₂] [Module R₂ M₂]
 
 variable {σ₁₂ : R →+* R₂}
 
+#print LinearMap.eqOn_span /-
 /-- If two linear maps are equal on a set `s`, then they are equal on `submodule.span s`.
 
 See also `linear_map.eq_on_span'` for a version using `set.eq_on`. -/
 theorem eqOn_span {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (H : Set.EqOn f g s) ⦃x⦄ (h : x ∈ span R s) :
     f x = g x := by apply span_induction h H <;> simp (config := { contextual := true })
 #align linear_map.eq_on_span LinearMap.eqOn_span
+-/
 
+#print LinearMap.eqOn_span' /-
 /-- If two linear maps are equal on a set `s`, then they are equal on `submodule.span s`.
 
 This version uses `set.eq_on`, and the hidden argument will expand to `h : x ∈ (span R s : set M)`.
@@ -1001,19 +1179,24 @@ theorem eqOn_span' {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (H : Set.EqOn
     Set.EqOn f g (span R s : Set M) :=
   eqOn_span H
 #align linear_map.eq_on_span' LinearMap.eqOn_span'
+-/
 
+#print LinearMap.ext_on /-
 /-- If `s` generates the whole module and linear maps `f`, `g` are equal on `s`, then they are
 equal. -/
 theorem ext_on {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (hv : span R s = ⊤) (h : Set.EqOn f g s) : f = g :=
   LinearMap.ext fun x => eqOn_span h (eq_top_iff'.1 hv _)
 #align linear_map.ext_on LinearMap.ext_on
+-/
 
+#print LinearMap.ext_on_range /-
 /-- If the range of `v : ι → M` generates the whole module and linear maps `f`, `g` are equal at
 each `v i`, then they are equal. -/
 theorem ext_on_range {ι : Type _} {v : ι → M} {f g : M →ₛₗ[σ₁₂] M₂} (hv : span R (Set.range v) = ⊤)
     (h : ∀ i, f (v i) = g (v i)) : f = g :=
   ext_on hv (Set.forall_range_iff.2 h)
 #align linear_map.ext_on_range LinearMap.ext_on_range
+-/
 
 end AddCommMonoid
 
@@ -1021,9 +1204,11 @@ section NoZeroDivisors
 
 variable (R M) [Ring R] [AddCommGroup M] [Module R M] [NoZeroSMulDivisors R M]
 
+#print LinearMap.ker_toSpanSingleton /-
 theorem ker_toSpanSingleton {x : M} (h : x ≠ 0) : (toSpanSingleton R M x).ker = ⊥ :=
   SetLike.ext fun c => smul_eq_zero.trans <| or_iff_left_of_imp fun h' => (h h').elim
 #align linear_map.ker_to_span_singleton LinearMap.ker_toSpanSingleton
+-/
 
 end NoZeroDivisors
 
@@ -1035,6 +1220,7 @@ noncomputable section
 
 open scoped Classical
 
+#print LinearMap.span_singleton_sup_ker_eq_top /-
 theorem span_singleton_sup_ker_eq_top (f : V →ₗ[K] K) {x : V} (hx : f x ≠ 0) :
     (K ∙ x) ⊔ f.ker = ⊤ :=
   eq_top_iff.2 fun y hy =>
@@ -1045,6 +1231,7 @@ theorem span_singleton_sup_ker_eq_top (f : V →ₗ[K] K) {x : V} (hx : f x ≠
             mul_one, sub_self],
           by simp only [add_sub_cancel'_right]⟩⟩
 #align linear_map.span_singleton_sup_ker_eq_top LinearMap.span_singleton_sup_ker_eq_top
+-/
 
 end Field
 
@@ -1056,6 +1243,7 @@ namespace LinearEquiv
 
 variable (R M) [Ring R] [AddCommGroup M] [Module R M] [NoZeroSMulDivisors R M] (x : M) (h : x ≠ 0)
 
+#print LinearEquiv.toSpanNonzeroSingleton /-
 /-- Given a nonzero element `x` of a torsion-free module `M` over a ring `R`, the natural
 isomorphism from `R` to the span of `x` given by $r \mapsto r \cdot x$. -/
 def toSpanNonzeroSingleton : R ≃ₗ[R] R ∙ x :=
@@ -1064,7 +1252,9 @@ def toSpanNonzeroSingleton : R ≃ₗ[R] R ∙ x :=
       (ker_eq_bot.1 <| ker_toSpanSingleton R M h))
     (LinearEquiv.ofEq (toSpanSingleton R M x).range (R ∙ x) (span_singleton_eq_range R M x).symm)
 #align linear_equiv.to_span_nonzero_singleton LinearEquiv.toSpanNonzeroSingleton
+-/
 
+#print LinearEquiv.toSpanNonzeroSingleton_one /-
 theorem toSpanNonzeroSingleton_one :
     LinearEquiv.toSpanNonzeroSingleton R M x h 1 =
       (⟨x, Submodule.mem_span_singleton_self x⟩ : R ∙ x) :=
@@ -1073,20 +1263,27 @@ theorem toSpanNonzeroSingleton_one :
   have : ↑(to_span_nonzero_singleton R M x h 1) = to_span_singleton R M x 1 := rfl
   rw [this, to_span_singleton_one, Submodule.coe_mk]
 #align linear_equiv.to_span_nonzero_singleton_one LinearEquiv.toSpanNonzeroSingleton_one
+-/
 
+#print LinearEquiv.coord /-
 /-- Given a nonzero element `x` of a torsion-free module `M` over a ring `R`, the natural
 isomorphism from the span of `x` to `R` given by $r \cdot x \mapsto r$. -/
 abbrev coord : (R ∙ x) ≃ₗ[R] R :=
   (toSpanNonzeroSingleton R M x h).symm
 #align linear_equiv.coord LinearEquiv.coord
+-/
 
+#print LinearEquiv.coord_self /-
 theorem coord_self : (coord R M x h) (⟨x, Submodule.mem_span_singleton_self x⟩ : R ∙ x) = 1 := by
   rw [← to_span_nonzero_singleton_one R M x h, LinearEquiv.symm_apply_apply]
 #align linear_equiv.coord_self LinearEquiv.coord_self
+-/
 
+#print LinearEquiv.coord_apply_smul /-
 theorem coord_apply_smul (y : Submodule.span R ({x} : Set M)) : coord R M x h y • x = y :=
   Subtype.ext_iff.1 <| (toSpanNonzeroSingleton R M x h).apply_symm_apply _
 #align linear_equiv.coord_apply_smul LinearEquiv.coord_apply_smul
+-/
 
 end LinearEquiv
 

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

@@ -858,7 +858,6 @@ theorem span_neg (s : Set M) : span R (-s) = span R s :=
     span R (-s) = span R ((-LinearMap.id : M →ₗ[R] M) '' s) := by simp
     _ = map (-LinearMap.id) (span R s) := ((-LinearMap.id).map_span _).symm
     _ = span R s := by simp
-    
 #align submodule.span_neg Submodule.span_neg
 
 theorem mem_span_insert' {x y} {s : Set M} :

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

@@ -54,7 +54,7 @@ variable (R)
 #print Submodule.span /-
 /-- The span of a set `s ⊆ M` is the smallest submodule of M that contains `s`. -/
 def span (s : Set M) : Submodule R M :=
-  sInf { p | s ⊆ p }
+  sInf {p | s ⊆ p}
 #align submodule.span Submodule.span
 -/
 
@@ -722,9 +722,9 @@ instance : IsCompactlyGenerated (Submodule R M) :=
 
 /-- A submodule is equal to the supremum of the spans of the submodule's nonzero elements. -/
 theorem submodule_eq_sSup_le_nonzero_spans (p : Submodule R M) :
-    p = sSup { T : Submodule R M | ∃ (m : M) (hm : m ∈ p) (hz : m ≠ 0), T = span R {m} } :=
+    p = sSup {T : Submodule R M | ∃ (m : M) (hm : m ∈ p) (hz : m ≠ 0), T = span R {m}} :=
   by
-  let S := { T : Submodule R M | ∃ (m : M) (hm : m ∈ p) (hz : m ≠ 0), T = span R {m} }
+  let S := {T : Submodule R M | ∃ (m : M) (hm : m ∈ p) (hz : m ≠ 0), T = span R {m}}
   apply le_antisymm
   · intro m hm; by_cases h : m = 0
     · rw [h]; simp

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

@@ -366,7 +366,7 @@ variable {p p'}
 
 theorem mem_sup : x ∈ p ⊔ p' ↔ ∃ y ∈ p, ∃ z ∈ p', y + z = x :=
   ⟨fun h => by
-    rw [← span_eq p, ← span_eq p', ← span_union] at h
+    rw [← span_eq p, ← span_eq p', ← span_union] at h 
     apply span_induction h
     · rintro y (h | h)
       · exact ⟨y, h, 0, by simp, by simp⟩
@@ -380,7 +380,7 @@ theorem mem_sup : x ∈ p ⊔ p' ↔ ∃ y ∈ p, ∃ z ∈ p', y + z = x :=
       exact add_mem ((le_sup_left : p ≤ p ⊔ p') hy) ((le_sup_right : p' ≤ p ⊔ p') hz)⟩
 #align submodule.mem_sup Submodule.mem_sup
 
-theorem mem_sup' : x ∈ p ⊔ p' ↔ ∃ (y : p)(z : p'), (y : M) + z = x :=
+theorem mem_sup' : x ∈ p ⊔ p' ↔ ∃ (y : p) (z : p'), (y : M) + z = x :=
   mem_sup.trans <| by simp only [SetLike.exists, coe_mk]
 #align submodule.mem_sup' Submodule.mem_sup'
 
@@ -417,7 +417,7 @@ theorem nontrivial_span_singleton {x : M} (h : x ≠ 0) : Nontrivial (R ∙ x) :
   ⟨by
     use 0, x, Submodule.mem_span_singleton_self x
     intro H
-    rw [eq_comm, Submodule.mk_eq_zero] at H
+    rw [eq_comm, Submodule.mk_eq_zero] at H 
     exact h H⟩
 #align submodule.nontrivial_span_singleton Submodule.nontrivial_span_singleton
 
@@ -487,7 +487,7 @@ theorem disjoint_span_singleton {K E : Type _} [DivisionRing K] [AddCommGroup E]
   obtain ⟨c, rfl⟩ := mem_span_singleton.1 hyx
   by_cases hc : c = 0
   · rw [hc, zero_smul]
-  · rw [s.smul_mem_iff hc] at hy
+  · rw [s.smul_mem_iff hc] at hy 
     rw [H hy, smul_zero]
 #align submodule.disjoint_span_singleton Submodule.disjoint_span_singleton
 
@@ -584,9 +584,9 @@ theorem span_singleton_eq_span_singleton {R M : Type _} [Ring R] [AddCommGroup M
   · intro hxy
     cases' mem_span_singleton.mp (by rw [hxy]; apply mem_span_singleton_self) with v hv
     cases' mem_span_singleton.mp (by rw [← hxy]; apply mem_span_singleton_self) with i hi
-    have vi : v * i = 1 := by rw [← one_smul R y, ← hi, smul_smul] at hv;
+    have vi : v * i = 1 := by rw [← one_smul R y, ← hi, smul_smul] at hv ;
       exact smul_left_injective R hy hv
-    have iv : i * v = 1 := by rw [← one_smul R x, ← hv, smul_smul] at hi;
+    have iv : i * v = 1 := by rw [← one_smul R x, ← hv, smul_smul] at hi ;
       exact smul_left_injective R hx hi
     exact ⟨⟨v, i, vi, iv⟩, hv⟩
   · rintro ⟨v, rfl⟩
@@ -655,7 +655,7 @@ theorem iSup_induction {ι : Sort _} (p : ι → Submodule R M) {C : M → Prop}
     (hx : x ∈ ⨆ i, p i) (hp : ∀ (i), ∀ x ∈ p i, C x) (h0 : C 0)
     (hadd : ∀ x y, C x → C y → C (x + y)) : C x :=
   by
-  rw [← mem_to_add_submonoid, supr_to_add_submonoid] at hx
+  rw [← mem_to_add_submonoid, supr_to_add_submonoid] at hx 
   exact AddSubmonoid.iSup_induction _ hx hp h0 hadd
 #align submodule.supr_induction Submodule.iSup_induction
 
@@ -687,7 +687,7 @@ theorem singleton_span_isCompactElement (x : M) :
   intro d hemp hdir hsup
   have : x ∈ Sup d := (set_like.le_def.mp hsup) (mem_span_singleton_self x)
   obtain ⟨y, ⟨hyd, hxy⟩⟩ := (mem_Sup_of_directed hemp hdir).mp this
-  exact ⟨y, ⟨hyd, by simpa only [span_le, singleton_subset_iff] ⟩⟩
+  exact ⟨y, ⟨hyd, by simpa only [span_le, singleton_subset_iff]⟩⟩
 #align submodule.singleton_span_is_compact_element Submodule.singleton_span_isCompactElement
 -/
 
@@ -722,9 +722,9 @@ instance : IsCompactlyGenerated (Submodule R M) :=
 
 /-- A submodule is equal to the supremum of the spans of the submodule's nonzero elements. -/
 theorem submodule_eq_sSup_le_nonzero_spans (p : Submodule R M) :
-    p = sSup { T : Submodule R M | ∃ (m : M)(hm : m ∈ p)(hz : m ≠ 0), T = span R {m} } :=
+    p = sSup { T : Submodule R M | ∃ (m : M) (hm : m ∈ p) (hz : m ≠ 0), T = span R {m} } :=
   by
-  let S := { T : Submodule R M | ∃ (m : M)(hm : m ∈ p)(hz : m ≠ 0), T = span R {m} }
+  let S := { T : Submodule R M | ∃ (m : M) (hm : m ∈ p) (hz : m ≠ 0), T = span R {m} }
   apply le_antisymm
   · intro m hm; by_cases h : m = 0
     · rw [h]; simp
@@ -871,7 +871,7 @@ theorem mem_span_insert' {x y} {s : Set M} :
 
 instance : IsModularLattice (Submodule R M) :=
   ⟨fun x y z xz a ha => by
-    rw [mem_inf, mem_sup] at ha
+    rw [mem_inf, mem_sup] at ha 
     rcases ha with ⟨⟨b, hb, c, hc, rfl⟩, haz⟩
     rw [mem_sup]
     refine' ⟨b, hb, c, mem_inf.2 ⟨hc, _⟩, rfl⟩

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

@@ -35,7 +35,7 @@ namespace Submodule
 
 open Function Set
 
-open Pointwise
+open scoped Pointwise
 
 section AddCommMonoid
 
@@ -762,7 +762,7 @@ theorem mem_iSup {ι : Sort _} (p : ι → Submodule R M) {m : M} :
 
 section
 
-open Classical
+open scoped Classical
 
 #print Submodule.mem_span_finite_of_mem_span /-
 /-- For every element in the span of a set, there exists a finite subset of the set
@@ -1034,7 +1034,7 @@ variable {K V} [Field K] [AddCommGroup V] [Module K V]
 
 noncomputable section
 
-open Classical
+open scoped Classical
 
 theorem span_singleton_sup_ker_eq_top (f : V →ₗ[K] K) {x : V} (hx : f x ≠ 0) :
     (K ∙ x) ⊔ f.ker = ⊤ :=

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

@@ -73,41 +73,17 @@ theorem subset_span : s ⊆ span R s := fun x h => mem_span.2 fun p hp => hp h
 #align submodule.subset_span Submodule.subset_span
 -/
 
-/- warning: submodule.span_le -> Submodule.span_le is a dubious translation:
-lean 3 declaration is
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 theorem span_le {p} : span R s ≤ p ↔ s ⊆ p :=
   ⟨Subset.trans subset_span, fun ss x h => mem_span.1 h _ ss⟩
 #align submodule.span_le Submodule.span_le
 
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 theorem span_mono (h : s ⊆ t) : span R s ≤ span R t :=
   span_le.2 <| Subset.trans h subset_span
 #align submodule.span_mono Submodule.span_mono
 
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 theorem span_monotone : Monotone (span R : Set M → Submodule R M) := fun _ _ => span_mono
 #align submodule.span_monotone Submodule.span_monotone
 
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 theorem span_eq_of_le (h₁ : s ⊆ p) (h₂ : p ≤ span R s) : span R s = p :=
   le_antisymm (span_le.2 h₁) h₂
 #align submodule.span_eq_of_le Submodule.span_eq_of_le
@@ -124,12 +100,6 @@ theorem span_eq_span (hs : s ⊆ span R t) (ht : t ⊆ span R s) : span R s = sp
 #align submodule.span_eq_span Submodule.span_eq_span
 -/
 
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 /-- A version of `submodule.span_eq` for when the span is by a smaller ring. -/
 @[simp]
 theorem span_coe_eq_restrictScalars [Semiring S] [SMul S R] [Module S M] [IsScalarTower S R M] :
@@ -137,9 +107,6 @@ theorem span_coe_eq_restrictScalars [Semiring S] [SMul S R] [Module S M] [IsScal
   span_eq (p.restrictScalars S)
 #align submodule.span_coe_eq_restrict_scalars Submodule.span_coe_eq_restrictScalars
 
-/- warning: submodule.map_span -> Submodule.map_span is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map_span Submodule.map_spanₓ'. -/
 theorem map_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (s : Set M) :
     (span R s).map f = span R₂ (f '' s) :=
   Eq.symm <|
@@ -147,15 +114,9 @@ theorem map_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (
       map_le_iff_le_comap.2 <| span_le.2 fun x hx => subset_span ⟨x, hx, rfl⟩
 #align submodule.map_span Submodule.map_span
 
-/- warning: linear_map.map_span -> LinearMap.map_span is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.map_span LinearMap.map_spanₓ'. -/
 alias Submodule.map_span ← _root_.linear_map.map_span
 #align linear_map.map_span LinearMap.map_span
 
-/- warning: submodule.map_span_le -> Submodule.map_span_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map_span_le Submodule.map_span_leₓ'. -/
 theorem map_span_le [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (s : Set M) (N : Submodule R₂ M₂) :
     map f (span R s) ≤ N ↔ ∀ m ∈ s, f m ∈ N :=
   by
@@ -163,18 +124,9 @@ theorem map_span_le [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂
   exact Iff.rfl
 #align submodule.map_span_le Submodule.map_span_le
 
-/- warning: linear_map.map_span_le -> LinearMap.map_span_le is a dubious translation:
-<too large>
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 alias Submodule.map_span_le ← _root_.linear_map.map_span_le
 #align linear_map.map_span_le LinearMap.map_span_le
 
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 @[simp]
 theorem span_insert_zero : span R (insert (0 : M) s) = span R s :=
   by
@@ -183,59 +135,29 @@ theorem span_insert_zero : span R (insert (0 : M) s) = span R s :=
   exact ⟨by simp only [SetLike.mem_coe, Submodule.zero_mem], Submodule.subset_span⟩
 #align submodule.span_insert_zero Submodule.span_insert_zero
 
-/- warning: submodule.span_preimage_le -> Submodule.span_preimage_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.span_preimage_le Submodule.span_preimage_leₓ'. -/
 -- See also `span_preimage_eq` below.
 theorem span_preimage_le (f : M →ₛₗ[σ₁₂] M₂) (s : Set M₂) :
     span R (f ⁻¹' s) ≤ (span R₂ s).comap f := by rw [span_le, comap_coe];
   exact preimage_mono subset_span
 #align submodule.span_preimage_le Submodule.span_preimage_le
 
-/- warning: linear_map.span_preimage_le -> LinearMap.span_preimage_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.span_preimage_le LinearMap.span_preimage_leₓ'. -/
 alias Submodule.span_preimage_le ← _root_.linear_map.span_preimage_le
 #align linear_map.span_preimage_le LinearMap.span_preimage_le
 
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 theorem closure_subset_span {s : Set M} : (AddSubmonoid.closure s : Set M) ⊆ span R s :=
   (@AddSubmonoid.closure_le _ _ _ (span R s).toAddSubmonoid).mpr subset_span
 #align submodule.closure_subset_span Submodule.closure_subset_span
 
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 theorem closure_le_toAddSubmonoid_span {s : Set M} :
     AddSubmonoid.closure s ≤ (span R s).toAddSubmonoid :=
   closure_subset_span
 #align submodule.closure_le_to_add_submonoid_span Submodule.closure_le_toAddSubmonoid_span
 
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 @[simp]
 theorem span_closure {s : Set M} : span R (AddSubmonoid.closure s : Set M) = span R s :=
   le_antisymm (span_le.mpr closure_subset_span) (span_mono AddSubmonoid.subset_closure)
 #align submodule.span_closure Submodule.span_closure
 
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-Case conversion may be inaccurate. Consider using '#align submodule.span_induction Submodule.span_inductionₓ'. -/
 /-- An induction principle for span membership. If `p` holds for 0 and all elements of `s`, and is
 preserved under addition and scalar multiplication, then `p` holds for all elements of the span of
 `s`. -/
@@ -245,12 +167,6 @@ theorem span_induction {p : M → Prop} (h : x ∈ span R s) (Hs : ∀ x ∈ s,
   (@span_le _ _ _ _ _ _ ⟨p, H1, H0, H2⟩).2 Hs h
 #align submodule.span_induction Submodule.span_induction
 
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-Case conversion may be inaccurate. Consider using '#align submodule.span_induction' Submodule.span_induction'ₓ'. -/
 /-- A dependent version of `submodule.span_induction`. -/
 theorem span_induction' {p : ∀ x, x ∈ span R s → Prop} (Hs : ∀ (x) (h : x ∈ s), p x (subset_span h))
     (H0 : p 0 (Submodule.zero_mem _))
@@ -267,12 +183,6 @@ theorem span_induction' {p : ∀ x, x ∈ span R s → Prop} (Hs : ∀ (x) (h :
       fun r x hx => Exists.elim hx fun hx' hx => ⟨smul_mem _ _ hx', H2 r _ _ hx⟩
 #align submodule.span_induction' Submodule.span_induction'
 
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-Case conversion may be inaccurate. Consider using '#align submodule.span_span_coe_preimage Submodule.span_span_coe_preimageₓ'. -/
 @[simp]
 theorem span_span_coe_preimage : span R ((coe : span R s → M) ⁻¹' s) = ⊤ :=
   eq_top_iff.2 fun x =>
@@ -296,23 +206,11 @@ theorem span_nat_eq_addSubmonoid_closure (s : Set M) :
 #align submodule.span_nat_eq_add_submonoid_closure Submodule.span_nat_eq_addSubmonoid_closure
 -/
 
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 @[simp]
 theorem span_nat_eq (s : AddSubmonoid M) : (span ℕ (s : Set M)).toAddSubmonoid = s := by
   rw [span_nat_eq_add_submonoid_closure, s.closure_eq]
 #align submodule.span_nat_eq Submodule.span_nat_eq
 
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 theorem span_int_eq_addSubgroup_closure {M : Type _} [AddCommGroup M] (s : Set M) :
     (span ℤ s).toAddSubgroup = AddSubgroup.closure s :=
   Eq.symm <|
@@ -321,12 +219,6 @@ theorem span_int_eq_addSubgroup_closure {M : Type _} [AddCommGroup M] (s : Set M
         (fun _ _ => AddSubgroup.add_mem _) fun _ _ _ => AddSubgroup.zsmul_mem _ ‹_› _
 #align submodule.span_int_eq_add_subgroup_closure Submodule.span_int_eq_addSubgroup_closure
 
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 @[simp]
 theorem span_int_eq {M : Type _} [AddCommGroup M] (s : AddSubgroup M) :
     (span ℤ (s : Set M)).toAddSubgroup = s := by rw [span_int_eq_add_subgroup_closure, s.closure_eq]
@@ -336,12 +228,6 @@ section
 
 variable (R M)
 
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 /-- `span` forms a Galois insertion with the coercion from submodule to set. -/
 protected def gi : GaloisInsertion (@span R M _ _ _) coe
     where
@@ -353,54 +239,24 @@ protected def gi : GaloisInsertion (@span R M _ _ _) coe
 
 end
 
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 @[simp]
 theorem span_empty : span R (∅ : Set M) = ⊥ :=
   (Submodule.gi R M).gc.l_bot
 #align submodule.span_empty Submodule.span_empty
 
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 @[simp]
 theorem span_univ : span R (univ : Set M) = ⊤ :=
   eq_top_iff.2 <| SetLike.le_def.2 <| subset_span
 #align submodule.span_univ Submodule.span_univ
 
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 theorem span_union (s t : Set M) : span R (s ∪ t) = span R s ⊔ span R t :=
   (Submodule.gi R M).gc.l_sup
 #align submodule.span_union Submodule.span_union
 
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 theorem span_iUnion {ι} (s : ι → Set M) : span R (⋃ i, s i) = ⨆ i, span R (s i) :=
   (Submodule.gi R M).gc.l_iSup
 #align submodule.span_Union Submodule.span_iUnion
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 theorem span_iUnion₂ {ι} {κ : ι → Sort _} (s : ∀ i, κ i → Set M) :
@@ -408,31 +264,13 @@ theorem span_iUnion₂ {ι} {κ : ι → Sort _} (s : ∀ i, κ i → Set M) :
   (Submodule.gi R M).gc.l_iSup₂
 #align submodule.span_Union₂ Submodule.span_iUnion₂
 
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 theorem span_attach_biUnion [DecidableEq M] {α : Type _} (s : Finset α) (f : s → Finset M) :
     span R (s.attach.biUnion f : Set M) = ⨆ x, span R (f x) := by simpa [span_Union]
 #align submodule.span_attach_bUnion Submodule.span_attach_biUnion
 
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 theorem sup_span : p ⊔ span R s = span R (p ∪ s) := by rw [Submodule.span_union, p.span_eq]
 #align submodule.sup_span Submodule.sup_span
 
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 theorem span_sup : span R s ⊔ p = span R (s ∪ p) := by rw [Submodule.span_union, p.span_eq]
 #align submodule.span_sup Submodule.span_sup
 
@@ -442,32 +280,14 @@ notation:1000
 character `•` U+2022 and the matrix multiplication character `⬝` U+2B1D. -/
 R " ∙ " x => span R (@singleton _ _ Set.hasSingleton x)
 
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 theorem span_eq_iSup_of_singleton_spans (s : Set M) : span R s = ⨆ x ∈ s, R ∙ x := by
   simp only [← span_Union, Set.biUnion_of_singleton s]
 #align submodule.span_eq_supr_of_singleton_spans Submodule.span_eq_iSup_of_singleton_spans
 
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 theorem span_range_eq_iSup {ι : Type _} {v : ι → M} : span R (range v) = ⨆ i, R ∙ v i := by
   rw [span_eq_supr_of_singleton_spans, iSup_range]
 #align submodule.span_range_eq_supr Submodule.span_range_eq_iSup
 
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 theorem span_smul_le (s : Set M) (r : R) : span R (r • s) ≤ span R s :=
   by
   rw [span_le]
@@ -496,12 +316,6 @@ theorem span_smul_eq_of_isUnit (s : Set M) (r : R) (hr : IsUnit r) : span R (r 
 #align submodule.span_smul_eq_of_is_unit Submodule.span_smul_eq_of_isUnit
 -/
 
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 @[simp]
 theorem coe_iSup_of_directed {ι} [hι : Nonempty ι] (S : ι → Submodule R M)
     (H : Directed (· ≤ ·) S) : ((iSup S : Submodule R M) : Set M) = ⋃ i, S i :=
@@ -517,23 +331,11 @@ theorem coe_iSup_of_directed {ι} [hι : Nonempty ι] (S : ι → Submodule R M)
   · exact fun a x i hi => ⟨i, smul_mem _ a hi⟩
 #align submodule.coe_supr_of_directed Submodule.coe_iSup_of_directed
 
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 @[simp]
 theorem mem_iSup_of_directed {ι} [Nonempty ι] (S : ι → Submodule R M) (H : Directed (· ≤ ·) S) {x} :
     x ∈ iSup S ↔ ∃ i, x ∈ S i := by rw [← SetLike.mem_coe, coe_supr_of_directed S H, mem_Union]; rfl
 #align submodule.mem_supr_of_directed Submodule.mem_iSup_of_directed
 
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-Case conversion may be inaccurate. Consider using '#align submodule.mem_Sup_of_directed Submodule.mem_sSup_of_directedₓ'. -/
 theorem mem_sSup_of_directed {s : Set (Submodule R M)} {z} (hs : s.Nonempty)
     (hdir : DirectedOn (· ≤ ·) s) : z ∈ sSup s ↔ ∃ y ∈ s, z ∈ y :=
   by
@@ -541,23 +343,11 @@ theorem mem_sSup_of_directed {s : Set (Submodule R M)} {z} (hs : s.Nonempty)
   simp only [sSup_eq_iSup', mem_supr_of_directed _ hdir.directed_coe, SetCoe.exists, Subtype.coe_mk]
 #align submodule.mem_Sup_of_directed Submodule.mem_sSup_of_directed
 
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 @[norm_cast, simp]
 theorem coe_iSup_of_chain (a : ℕ →o Submodule R M) : (↑(⨆ k, a k) : Set M) = ⋃ k, (a k : Set M) :=
   coe_iSup_of_directed a a.Monotone.directed_le
 #align submodule.coe_supr_of_chain Submodule.coe_iSup_of_chain
 
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 /-- We can regard `coe_supr_of_chain` as the statement that `coe : (submodule R M) → set M` is
 Scott continuous for the ω-complete partial order induced by the complete lattice structures. -/
 theorem coe_scott_continuous :
@@ -565,12 +355,6 @@ theorem coe_scott_continuous :
   ⟨SetLike.coe_mono, coe_iSup_of_chain⟩
 #align submodule.coe_scott_continuous Submodule.coe_scott_continuous
 
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-Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_of_chain Submodule.mem_iSup_of_chainₓ'. -/
 @[simp]
 theorem mem_iSup_of_chain (a : ℕ →o Submodule R M) (m : M) : (m ∈ ⨆ k, a k) ↔ ∃ k, m ∈ a k :=
   mem_iSup_of_directed a a.Monotone.directed_le
@@ -580,12 +364,6 @@ section
 
 variable {p p'}
 
-/- warning: submodule.mem_sup -> Submodule.mem_sup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align submodule.mem_sup Submodule.mem_supₓ'. -/
 theorem mem_sup : x ∈ p ⊔ p' ↔ ∃ y ∈ p, ∃ z ∈ p', y + z = x :=
   ⟨fun h => by
     rw [← span_eq p, ← span_eq p', ← span_union] at h
@@ -602,31 +380,16 @@ theorem mem_sup : x ∈ p ⊔ p' ↔ ∃ y ∈ p, ∃ z ∈ p', y + z = x :=
       exact add_mem ((le_sup_left : p ≤ p ⊔ p') hy) ((le_sup_right : p' ≤ p ⊔ p') hz)⟩
 #align submodule.mem_sup Submodule.mem_sup
 
-/- warning: submodule.mem_sup' -> Submodule.mem_sup' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mem_sup' Submodule.mem_sup'ₓ'. -/
 theorem mem_sup' : x ∈ p ⊔ p' ↔ ∃ (y : p)(z : p'), (y : M) + z = x :=
   mem_sup.trans <| by simp only [SetLike.exists, coe_mk]
 #align submodule.mem_sup' Submodule.mem_sup'
 
 variable (p p')
 
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-Case conversion may be inaccurate. Consider using '#align submodule.coe_sup Submodule.coe_supₓ'. -/
 theorem coe_sup : ↑(p ⊔ p') = (p + p' : Set M) := by ext;
   rw [SetLike.mem_coe, mem_sup, Set.mem_add]; simp
 #align submodule.coe_sup Submodule.coe_sup
 
-/- warning: submodule.sup_to_add_submonoid -> Submodule.sup_toAddSubmonoid is a dubious translation:
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 theorem sup_toAddSubmonoid : (p ⊔ p').toAddSubmonoid = p.toAddSubmonoid ⊔ p'.toAddSubmonoid :=
   by
   ext x
@@ -634,12 +397,6 @@ theorem sup_toAddSubmonoid : (p ⊔ p').toAddSubmonoid = p.toAddSubmonoid ⊔ p'
   rfl
 #align submodule.sup_to_add_submonoid Submodule.sup_toAddSubmonoid
 
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 theorem sup_toAddSubgroup {R M : Type _} [Ring R] [AddCommGroup M] [Module R M]
     (p p' : Submodule R M) : (p ⊔ p').toAddSubgroup = p.toAddSubgroup ⊔ p'.toAddSubgroup :=
   by
@@ -656,12 +413,6 @@ theorem mem_span_singleton_self (x : M) : x ∈ R ∙ x :=
 #align submodule.mem_span_singleton_self Submodule.mem_span_singleton_self
 -/
 
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 theorem nontrivial_span_singleton {x : M} (h : x ≠ 0) : Nontrivial (R ∙ x) :=
   ⟨by
     use 0, x, Submodule.mem_span_singleton_self x
@@ -684,34 +435,16 @@ theorem mem_span_singleton {y : M} : (x ∈ R ∙ y) ↔ ∃ a : R, a • y = x
 #align submodule.mem_span_singleton Submodule.mem_span_singleton
 -/
 
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 theorem le_span_singleton_iff {s : Submodule R M} {v₀ : M} :
     (s ≤ R ∙ v₀) ↔ ∀ v ∈ s, ∃ r : R, r • v₀ = v := by simp_rw [SetLike.le_def, mem_span_singleton]
 #align submodule.le_span_singleton_iff Submodule.le_span_singleton_iff
 
 variable (R)
 
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 theorem span_singleton_eq_top_iff (x : M) : (R ∙ x) = ⊤ ↔ ∀ v, ∃ r : R, r • x = v := by
   rw [eq_top_iff, le_span_singleton_iff]; tauto
 #align submodule.span_singleton_eq_top_iff Submodule.span_singleton_eq_top_iff
 
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 @[simp]
 theorem span_zero_singleton : (R ∙ (0 : M)) = ⊥ := by ext; simp [mem_span_singleton, eq_comm]
 #align submodule.span_zero_singleton Submodule.span_zero_singleton
@@ -722,12 +455,6 @@ theorem span_singleton_eq_range (y : M) : ↑(R ∙ y) = range ((· • y) : R 
 #align submodule.span_singleton_eq_range Submodule.span_singleton_eq_range
 -/
 
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 theorem span_singleton_smul_le {S} [Monoid S] [SMul S R] [MulAction S M] [IsScalarTower S R M]
     (r : S) (x : M) : (R ∙ r • x) ≤ R ∙ x :=
   by
@@ -735,12 +462,6 @@ theorem span_singleton_smul_le {S} [Monoid S] [SMul S R] [MulAction S M] [IsScal
   exact smul_of_tower_mem _ _ (mem_span_singleton_self _)
 #align submodule.span_singleton_smul_le Submodule.span_singleton_smul_le
 
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 theorem span_singleton_group_smul_eq {G} [Group G] [SMul G R] [MulAction G M] [IsScalarTower G R M]
     (g : G) (x : M) : (R ∙ g • x) = R ∙ x :=
   by
@@ -751,12 +472,6 @@ theorem span_singleton_group_smul_eq {G} [Group G] [SMul G R] [MulAction G M] [I
 
 variable {R}
 
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 theorem span_singleton_smul_eq {r : R} (hr : IsUnit r) (x : M) : (R ∙ r • x) = R ∙ x :=
   by
   lift r to Rˣ using hr
@@ -764,12 +479,6 @@ theorem span_singleton_smul_eq {r : R} (hr : IsUnit r) (x : M) : (R ∙ r • x)
   exact span_singleton_group_smul_eq R r x
 #align submodule.span_singleton_smul_eq Submodule.span_singleton_smul_eq
 
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-Case conversion may be inaccurate. Consider using '#align submodule.disjoint_span_singleton Submodule.disjoint_span_singletonₓ'. -/
 theorem disjoint_span_singleton {K E : Type _} [DivisionRing K] [AddCommGroup E] [Module K E]
     {s : Submodule K E} {x : E} : Disjoint s (K ∙ x) ↔ x ∈ s → x = 0 :=
   by
@@ -782,12 +491,6 @@ theorem disjoint_span_singleton {K E : Type _} [DivisionRing K] [AddCommGroup E]
     rw [H hy, smul_zero]
 #align submodule.disjoint_span_singleton Submodule.disjoint_span_singleton
 
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 theorem disjoint_span_singleton' {K E : Type _} [DivisionRing K] [AddCommGroup E] [Module K E]
     {p : Submodule K E} {x : E} (x0 : x ≠ 0) : Disjoint p (K ∙ x) ↔ x ∉ p :=
   disjoint_span_singleton.trans ⟨fun h₁ h₂ => x0 (h₁ h₂), fun h₁ h₂ => (h₁ h₂).elim⟩
@@ -801,12 +504,6 @@ theorem mem_span_singleton_trans {x y z : M} (hxy : x ∈ R ∙ y) (hyz : y ∈
 #align submodule.mem_span_singleton_trans Submodule.mem_span_singleton_trans
 -/
 
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-Case conversion may be inaccurate. Consider using '#align submodule.mem_span_insert Submodule.mem_span_insertₓ'. -/
 theorem mem_span_insert {y} : x ∈ span R (insert y s) ↔ ∃ a : R, ∃ z ∈ span R s, x = a • y + z :=
   by
   simp only [← union_singleton, span_union, mem_sup, mem_span_singleton, exists_prop,
@@ -815,22 +512,10 @@ theorem mem_span_insert {y} : x ∈ span R (insert y s) ↔ ∃ a : R, ∃ z ∈
   simp only [eq_comm, add_comm, exists_and_left]
 #align submodule.mem_span_insert Submodule.mem_span_insert
 
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 theorem mem_span_pair {x y z : M} : z ∈ span R ({x, y} : Set M) ↔ ∃ a b : R, a • x + b • y = z := by
   simp_rw [mem_span_insert, mem_span_singleton, exists_prop, exists_exists_eq_and, eq_comm]
 #align submodule.mem_span_pair Submodule.mem_span_pair
 
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 theorem span_insert (x) (s : Set M) : span R (insert x s) = span R ({x} : Set M) ⊔ span R s := by
   rw [insert_eq, span_union]
 #align submodule.span_insert Submodule.span_insert
@@ -849,24 +534,12 @@ theorem span_span : span R (span R s : Set M) = span R s :=
 
 variable (R S s)
 
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 /-- If `R` is "smaller" ring than `S` then the span by `R` is smaller than the span by `S`. -/
 theorem span_le_restrictScalars [Semiring S] [SMul R S] [Module S M] [IsScalarTower R S M] :
     span R s ≤ (span S s).restrictScalars R :=
   Submodule.span_le.2 Submodule.subset_span
 #align submodule.span_le_restrict_scalars Submodule.span_le_restrictScalars
 
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 /-- A version of `submodule.span_le_restrict_scalars` with coercions. -/
 @[simp]
 theorem span_subset_span [Semiring S] [SMul R S] [Module S M] [IsScalarTower R S M] :
@@ -874,12 +547,6 @@ theorem span_subset_span [Semiring S] [SMul R S] [Module S M] [IsScalarTower R S
   span_le_restrictScalars R S s
 #align submodule.span_subset_span Submodule.span_subset_span
 
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 /-- Taking the span by a large ring of the span by the small ring is the same as taking the span
 by just the large ring. -/
 theorem span_span_of_tower [Semiring S] [SMul R S] [Module S M] [IsScalarTower R S M] :
@@ -889,45 +556,21 @@ theorem span_span_of_tower [Semiring S] [SMul R S] [Module S M] [IsScalarTower R
 
 variable {R S s}
 
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 theorem span_eq_bot : span R (s : Set M) = ⊥ ↔ ∀ x ∈ s, (x : M) = 0 :=
   eq_bot_iff.trans
     ⟨fun H x h => (mem_bot R).1 <| H <| subset_span h, fun H =>
       span_le.2 fun x h => (mem_bot R).2 <| H x h⟩
 #align submodule.span_eq_bot Submodule.span_eq_bot
 
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 @[simp]
 theorem span_singleton_eq_bot : (R ∙ x) = ⊥ ↔ x = 0 :=
   span_eq_bot.trans <| by simp
 #align submodule.span_singleton_eq_bot Submodule.span_singleton_eq_bot
 
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 @[simp]
 theorem span_zero : span R (0 : Set M) = ⊥ := by rw [← singleton_zero, span_singleton_eq_bot]
 #align submodule.span_zero Submodule.span_zero
 
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-Case conversion may be inaccurate. Consider using '#align submodule.span_singleton_eq_span_singleton Submodule.span_singleton_eq_span_singletonₓ'. -/
 theorem span_singleton_eq_span_singleton {R M : Type _} [Ring R] [AddCommGroup M] [Module R M]
     [NoZeroSMulDivisors R M] {x y : M} : ((R ∙ x) = R ∙ y) ↔ ∃ z : Rˣ, z • x = y :=
   by
@@ -950,18 +593,12 @@ theorem span_singleton_eq_span_singleton {R M : Type _} [Ring R] [AddCommGroup M
     rw [span_singleton_group_smul_eq]
 #align submodule.span_singleton_eq_span_singleton Submodule.span_singleton_eq_span_singleton
 
-/- warning: submodule.span_image -> Submodule.span_image is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.span_image Submodule.span_imageₓ'. -/
 @[simp]
 theorem span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) :
     span R₂ (f '' s) = map f (span R s) :=
   (map_span f s).symm
 #align submodule.span_image Submodule.span_image
 
-/- warning: submodule.apply_mem_span_image_of_mem_span -> Submodule.apply_mem_span_image_of_mem_span is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.apply_mem_span_image_of_mem_span Submodule.apply_mem_span_image_of_mem_spanₓ'. -/
 theorem apply_mem_span_image_of_mem_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) {x : M}
     {s : Set M} (h : x ∈ Submodule.span R s) : f x ∈ Submodule.span R₂ (f '' s) :=
   by
@@ -969,50 +606,26 @@ theorem apply_mem_span_image_of_mem_span [RingHomSurjective σ₁₂] (f : M →
   exact Submodule.mem_map_of_mem h
 #align submodule.apply_mem_span_image_of_mem_span Submodule.apply_mem_span_image_of_mem_span
 
-/- warning: submodule.map_subtype_span_singleton -> Submodule.map_subtype_span_singleton is a dubious translation:
-<too large>
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 @[simp]
 theorem map_subtype_span_singleton {p : Submodule R M} (x : p) :
     map p.Subtype (R ∙ x) = R ∙ (x : M) := by simp [← span_image]
 #align submodule.map_subtype_span_singleton Submodule.map_subtype_span_singleton
 
-/- warning: submodule.not_mem_span_of_apply_not_mem_span_image -> Submodule.not_mem_span_of_apply_not_mem_span_image is a dubious translation:
-<too large>
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 /-- `f` is an explicit argument so we can `apply` this theorem and obtain `h` as a new goal. -/
 theorem not_mem_span_of_apply_not_mem_span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) {x : M}
     {s : Set M} (h : f x ∉ Submodule.span R₂ (f '' s)) : x ∉ Submodule.span R s :=
   h.imp (apply_mem_span_image_of_mem_span f)
 #align submodule.not_mem_span_of_apply_not_mem_span_image Submodule.not_mem_span_of_apply_not_mem_span_image
 
-/- warning: submodule.supr_span -> Submodule.iSup_span is a dubious translation:
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 theorem iSup_span {ι : Sort _} (p : ι → Set M) : (⨆ i, span R (p i)) = span R (⋃ i, p i) :=
   le_antisymm (iSup_le fun i => span_mono <| subset_iUnion _ i) <|
     span_le.mpr <| iUnion_subset fun i m hm => mem_iSup_of_mem i <| subset_span hm
 #align submodule.supr_span Submodule.iSup_span
 
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 theorem iSup_eq_span {ι : Sort _} (p : ι → Submodule R M) : (⨆ i, p i) = span R (⋃ i, ↑(p i)) := by
   simp_rw [← supr_span, span_eq]
 #align submodule.supr_eq_span Submodule.iSup_eq_span
 
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 theorem iSup_toAddSubmonoid {ι : Sort _} (p : ι → Submodule R M) :
     (⨆ i, p i).toAddSubmonoid = ⨆ i, (p i).toAddSubmonoid :=
   by
@@ -1034,12 +647,6 @@ theorem iSup_toAddSubmonoid {ι : Sort _} (p : ι → Submodule R M) :
       exact AddSubmonoid.add_mem _ hx hy
 #align submodule.supr_to_add_submonoid Submodule.iSup_toAddSubmonoid
 
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 /-- An induction principle for elements of `⨆ i, p i`.
 If `C` holds for `0` and all elements of `p i` for all `i`, and is preserved under addition,
 then it holds for all elements of the supremum of `p`. -/
@@ -1052,9 +659,6 @@ theorem iSup_induction {ι : Sort _} (p : ι → Submodule R M) {C : M → Prop}
   exact AddSubmonoid.iSup_induction _ hx hp h0 hadd
 #align submodule.supr_induction Submodule.iSup_induction
 
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 /-- A dependent version of `submodule.supr_induction`. -/
 @[elab_as_elim]
 theorem iSup_induction' {ι : Sort _} (p : ι → Submodule R M) {C : ∀ x, (x ∈ ⨆ i, p i) → Prop}
@@ -1070,12 +674,6 @@ theorem iSup_induction' {ι : Sort _} (p : ι → Submodule R M) {C : ∀ x, (x
     refine' ⟨_, hadd _ _ _ _ Cx Cy⟩
 #align submodule.supr_induction' Submodule.iSup_induction'
 
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 @[simp]
 theorem span_singleton_le_iff_mem (m : M) (p : Submodule R M) : (R ∙ m) ≤ p ↔ m ∈ p := by
   rw [span_le, singleton_subset_iff, SetLike.mem_coe]
@@ -1122,12 +720,6 @@ instance : IsCompactlyGenerated (Submodule R M) :=
         apply singleton_span_is_compact_element, by
         rw [sSup_eq_iSup, iSup_image, ← span_eq_supr_of_singleton_spans, span_eq]⟩⟩⟩
 
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 /-- A submodule is equal to the supremum of the spans of the submodule's nonzero elements. -/
 theorem submodule_eq_sSup_le_nonzero_spans (p : Submodule R M) :
     p = sSup { T : Submodule R M | ∃ (m : M)(hm : m ∈ p)(hz : m ≠ 0), T = span R {m} } :=
@@ -1140,12 +732,6 @@ theorem submodule_eq_sSup_le_nonzero_spans (p : Submodule R M) :
   · rw [sSup_le_iff]; rintro S ⟨_, ⟨_, ⟨_, rfl⟩⟩⟩; rwa [span_singleton_le_iff_mem]
 #align submodule.submodule_eq_Sup_le_nonzero_spans Submodule.submodule_eq_sSup_le_nonzero_spans
 
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 theorem lt_sup_iff_not_mem {I : Submodule R M} {a : M} : (I < I ⊔ R ∙ a) ↔ a ∉ I :=
   by
   constructor
@@ -1167,12 +753,6 @@ theorem lt_sup_iff_not_mem {I : Submodule R M} {a : M} : (I < I ⊔ R ∙ a) ↔
       exact this (mem_span_singleton_self a)
 #align submodule.lt_sup_iff_not_mem Submodule.lt_sup_iff_not_mem
 
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 theorem mem_iSup {ι : Sort _} (p : ι → Submodule R M) {m : M} :
     (m ∈ ⨆ i, p i) ↔ ∀ N, (∀ i, p i ≤ N) → m ∈ N :=
   by
@@ -1211,12 +791,6 @@ end
 
 variable {M' : Type _} [AddCommMonoid M'] [Module R M'] (q₁ q₁' : Submodule R M')
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The product of two submodules is a submodule. -/
 def prod : Submodule R (M × M') :=
@@ -1226,83 +800,41 @@ def prod : Submodule R (M × M') :=
     smul_mem' := by rintro a ⟨x, y⟩ ⟨hx, hy⟩ <;> exact ⟨smul_mem _ a hx, smul_mem _ a hy⟩ }
 #align submodule.prod Submodule.prod
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
 theorem prod_coe : (prod p q₁ : Set (M × M')) = p ×ˢ q₁ :=
   rfl
 #align submodule.prod_coe Submodule.prod_coe
 
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 @[simp]
 theorem mem_prod {p : Submodule R M} {q : Submodule R M'} {x : M × M'} :
     x ∈ prod p q ↔ x.1 ∈ p ∧ x.2 ∈ q :=
   Set.mem_prod
 #align submodule.mem_prod Submodule.mem_prod
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem span_prod_le (s : Set M) (t : Set M') : span R (s ×ˢ t) ≤ prod (span R s) (span R t) :=
   span_le.2 <| Set.prod_mono subset_span subset_span
 #align submodule.span_prod_le Submodule.span_prod_le
 
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 @[simp]
 theorem prod_top : (prod ⊤ ⊤ : Submodule R (M × M')) = ⊤ := by ext <;> simp
 #align submodule.prod_top Submodule.prod_top
 
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 @[simp]
 theorem prod_bot : (prod ⊥ ⊥ : Submodule R (M × M')) = ⊥ := by ext ⟨x, y⟩ <;> simp [Prod.zero_eq_mk]
 #align submodule.prod_bot Submodule.prod_bot
 
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 theorem prod_mono {p p' : Submodule R M} {q q' : Submodule R M'} :
     p ≤ p' → q ≤ q' → prod p q ≤ prod p' q' :=
   prod_mono
 #align submodule.prod_mono Submodule.prod_mono
 
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 @[simp]
 theorem prod_inf_prod : prod p q₁ ⊓ prod p' q₁' = prod (p ⊓ p') (q₁ ⊓ q₁') :=
   SetLike.coe_injective Set.prod_inter_prod
 #align submodule.prod_inf_prod Submodule.prod_inf_prod
 
-/- warning: submodule.prod_sup_prod -> Submodule.prod_sup_prod is a dubious translation:
-<too large>
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 @[simp]
 theorem prod_sup_prod : prod p q₁ ⊔ prod p' q₁' = prod (p ⊔ p') (q₁ ⊔ q₁') :=
   by
@@ -1320,12 +852,6 @@ section AddCommGroup
 
 variable [Ring R] [AddCommGroup M] [Module R M]
 
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 @[simp]
 theorem span_neg (s : Set M) : span R (-s) = span R s :=
   calc
@@ -1335,12 +861,6 @@ theorem span_neg (s : Set M) : span R (-s) = span R s :=
     
 #align submodule.span_neg Submodule.span_neg
 
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 theorem mem_span_insert' {x y} {s : Set M} :
     x ∈ span R (insert y s) ↔ ∃ a : R, x + a • y ∈ span R s :=
   by
@@ -1372,9 +892,6 @@ variable {F : Type _} [sc : SemilinearMapClass F τ₁₂ M M₂]
 
 include sc
 
-/- warning: submodule.comap_map_eq -> Submodule.comap_map_eq is a dubious translation:
-<too large>
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 theorem comap_map_eq (f : F) (p : Submodule R M) : comap f (map f p) = p ⊔ LinearMap.ker f :=
   by
   refine' le_antisymm _ (sup_le (le_comap_map _ _) (comap_mono bot_le))
@@ -1382,9 +899,6 @@ theorem comap_map_eq (f : F) (p : Submodule R M) : comap f (map f p) = p ⊔ Lin
   exact mem_sup.2 ⟨y, hy, x - y, by simpa using sub_eq_zero.2 e.symm, by simp⟩
 #align submodule.comap_map_eq Submodule.comap_map_eq
 
-/- warning: submodule.comap_map_eq_self -> Submodule.comap_map_eq_self is a dubious translation:
-<too large>
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 theorem comap_map_eq_self {f : F} {p : Submodule R M} (h : LinearMap.ker f ≤ p) :
     comap f (map f p) = p := by rw [Submodule.comap_map_eq, sup_of_le_left h]
 #align submodule.comap_map_eq_self Submodule.comap_map_eq_self
@@ -1415,30 +929,18 @@ include R
 
 include sc
 
-/- warning: linear_map.map_le_map_iff -> LinearMap.map_le_map_iff is a dubious translation:
-<too large>
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 protected theorem map_le_map_iff (f : F) {p p'} : map f p ≤ map f p' ↔ p ≤ p' ⊔ ker f := by
   rw [map_le_iff_le_comap, Submodule.comap_map_eq]
 #align linear_map.map_le_map_iff LinearMap.map_le_map_iff
 
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 theorem map_le_map_iff' {f : F} (hf : ker f = ⊥) {p p'} : map f p ≤ map f p' ↔ p ≤ p' := by
   rw [LinearMap.map_le_map_iff, hf, sup_bot_eq]
 #align linear_map.map_le_map_iff' LinearMap.map_le_map_iff'
 
-/- warning: linear_map.map_injective -> LinearMap.map_injective is a dubious translation:
-<too large>
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 theorem map_injective {f : F} (hf : ker f = ⊥) : Injective (map f) := fun p p' h =>
   le_antisymm ((map_le_map_iff' hf).1 (le_of_eq h)) ((map_le_map_iff' hf).1 (ge_of_eq h))
 #align linear_map.map_injective LinearMap.map_injective
 
-/- warning: linear_map.map_eq_top_iff -> LinearMap.map_eq_top_iff is a dubious translation:
-<too large>
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 theorem map_eq_top_iff {f : F} (hf : range f = ⊤) {p : Submodule R M} :
     p.map f = ⊤ ↔ p ⊔ LinearMap.ker f = ⊤ := by
   simp_rw [← top_le_iff, ← hf, range_eq_map, LinearMap.map_le_map_iff]
@@ -1466,23 +968,11 @@ theorem span_singleton_eq_range (x : M) : (R ∙ x) = (toSpanSingleton R M x).ra
 #align linear_map.span_singleton_eq_range LinearMap.span_singleton_eq_range
 -/
 
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 @[simp]
 theorem toSpanSingleton_one (x : M) : toSpanSingleton R M x 1 = x :=
   one_smul _ _
 #align linear_map.to_span_singleton_one LinearMap.toSpanSingleton_one
 
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 @[simp]
 theorem toSpanSingleton_zero : toSpanSingleton R M 0 = 0 := by ext; simp
 #align linear_map.to_span_singleton_zero LinearMap.toSpanSingleton_zero
@@ -1497,9 +987,6 @@ variable [Semiring R₂] [AddCommMonoid M₂] [Module R₂ M₂]
 
 variable {σ₁₂ : R →+* R₂}
 
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 /-- If two linear maps are equal on a set `s`, then they are equal on `submodule.span s`.
 
 See also `linear_map.eq_on_span'` for a version using `set.eq_on`. -/
@@ -1507,9 +994,6 @@ theorem eqOn_span {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (H : Set.EqOn f
     f x = g x := by apply span_induction h H <;> simp (config := { contextual := true })
 #align linear_map.eq_on_span LinearMap.eqOn_span
 
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 /-- If two linear maps are equal on a set `s`, then they are equal on `submodule.span s`.
 
 This version uses `set.eq_on`, and the hidden argument will expand to `h : x ∈ (span R s : set M)`.
@@ -1519,18 +1003,12 @@ theorem eqOn_span' {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (H : Set.EqOn
   eqOn_span H
 #align linear_map.eq_on_span' LinearMap.eqOn_span'
 
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 /-- If `s` generates the whole module and linear maps `f`, `g` are equal on `s`, then they are
 equal. -/
 theorem ext_on {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (hv : span R s = ⊤) (h : Set.EqOn f g s) : f = g :=
   LinearMap.ext fun x => eqOn_span h (eq_top_iff'.1 hv _)
 #align linear_map.ext_on LinearMap.ext_on
 
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 /-- If the range of `v : ι → M` generates the whole module and linear maps `f`, `g` are equal at
 each `v i`, then they are equal. -/
 theorem ext_on_range {ι : Type _} {v : ι → M} {f g : M →ₛₗ[σ₁₂] M₂} (hv : span R (Set.range v) = ⊤)
@@ -1544,12 +1022,6 @@ section NoZeroDivisors
 
 variable (R M) [Ring R] [AddCommGroup M] [Module R M] [NoZeroSMulDivisors R M]
 
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_inst_4)) (Bot.bot.{u1} (Submodule.{u1, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (Submodule.instBotSubmodule.{u1, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R 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-Case conversion may be inaccurate. Consider using '#align linear_map.ker_to_span_singleton LinearMap.ker_toSpanSingletonₓ'. -/
 theorem ker_toSpanSingleton {x : M} (h : x ≠ 0) : (toSpanSingleton R M x).ker = ⊥ :=
   SetLike.ext fun c => smul_eq_zero.trans <| or_iff_left_of_imp fun h' => (h h').elim
 #align linear_map.ker_to_span_singleton LinearMap.ker_toSpanSingleton
@@ -1564,9 +1036,6 @@ noncomputable section
 
 open Classical
 
-/- warning: linear_map.span_singleton_sup_ker_eq_top -> LinearMap.span_singleton_sup_ker_eq_top is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.span_singleton_sup_ker_eq_top LinearMap.span_singleton_sup_ker_eq_topₓ'. -/
 theorem span_singleton_sup_ker_eq_top (f : V →ₗ[K] K) {x : V} (hx : f x ≠ 0) :
     (K ∙ x) ⊔ f.ker = ⊤ :=
   eq_top_iff.2 fun y hy =>
@@ -1588,12 +1057,6 @@ namespace LinearEquiv
 
 variable (R M) [Ring R] [AddCommGroup M] [Module R M] [NoZeroSMulDivisors R M] (x : M) (h : x ≠ 0)
 
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 /-- Given a nonzero element `x` of a torsion-free module `M` over a ring `R`, the natural
 isomorphism from `R` to the span of `x` given by $r \mapsto r \cdot x$. -/
 def toSpanNonzeroSingleton : R ≃ₗ[R] R ∙ x :=
@@ -1603,9 +1066,6 @@ def toSpanNonzeroSingleton : R ≃ₗ[R] R ∙ x :=
     (LinearEquiv.ofEq (toSpanSingleton R M x).range (R ∙ x) (span_singleton_eq_range R M x).symm)
 #align linear_equiv.to_span_nonzero_singleton LinearEquiv.toSpanNonzeroSingleton
 
-/- warning: linear_equiv.to_span_nonzero_singleton_one -> LinearEquiv.toSpanNonzeroSingleton_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_equiv.to_span_nonzero_singleton_one LinearEquiv.toSpanNonzeroSingleton_oneₓ'. -/
 theorem toSpanNonzeroSingleton_one :
     LinearEquiv.toSpanNonzeroSingleton R M x h 1 =
       (⟨x, Submodule.mem_span_singleton_self x⟩ : R ∙ x) :=
@@ -1615,21 +1075,12 @@ theorem toSpanNonzeroSingleton_one :
   rw [this, to_span_singleton_one, Submodule.coe_mk]
 #align linear_equiv.to_span_nonzero_singleton_one LinearEquiv.toSpanNonzeroSingleton_one
 
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-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Field.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (_inst_4 : M), (Ne.{succ u2} M _inst_4 (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2)))))))) -> (LinearEquiv.{u1, u1, u2, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))
-Case conversion may be inaccurate. Consider using '#align linear_equiv.coord LinearEquiv.coordₓ'. -/
 /-- Given a nonzero element `x` of a torsion-free module `M` over a ring `R`, the natural
 isomorphism from the span of `x` to `R` given by $r \cdot x \mapsto r$. -/
 abbrev coord : (R ∙ x) ≃ₗ[R] R :=
   (toSpanNonzeroSingleton R M x h).symm
 #align linear_equiv.coord LinearEquiv.coord
 
-/- warning: linear_equiv.coord_self -> LinearEquiv.coord_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_equiv.coord_self LinearEquiv.coord_selfₓ'. -/
 theorem coord_self : (coord R M x h) (⟨x, Submodule.mem_span_singleton_self x⟩ : R ∙ x) = 1 := by
   rw [← to_span_nonzero_singleton_one R M x h, LinearEquiv.symm_apply_apply]
 #align linear_equiv.coord_self LinearEquiv.coord_self

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

@@ -188,9 +188,7 @@ theorem span_insert_zero : span R (insert (0 : M) s) = span R s :=
 Case conversion may be inaccurate. Consider using '#align submodule.span_preimage_le Submodule.span_preimage_leₓ'. -/
 -- See also `span_preimage_eq` below.
 theorem span_preimage_le (f : M →ₛₗ[σ₁₂] M₂) (s : Set M₂) :
-    span R (f ⁻¹' s) ≤ (span R₂ s).comap f :=
-  by
-  rw [span_le, comap_coe]
+    span R (f ⁻¹' s) ≤ (span R₂ s).comap f := by rw [span_le, comap_coe];
   exact preimage_mono subset_span
 #align submodule.span_preimage_le Submodule.span_preimage_le
 
@@ -527,10 +525,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_of_directed Submodule.mem_iSup_of_directedₓ'. -/
 @[simp]
 theorem mem_iSup_of_directed {ι} [Nonempty ι] (S : ι → Submodule R M) (H : Directed (· ≤ ·) S) {x} :
-    x ∈ iSup S ↔ ∃ i, x ∈ S i :=
-  by
-  rw [← SetLike.mem_coe, coe_supr_of_directed S H, mem_Union]
-  rfl
+    x ∈ iSup S ↔ ∃ i, x ∈ S i := by rw [← SetLike.mem_coe, coe_supr_of_directed S H, mem_Union]; rfl
 #align submodule.mem_supr_of_directed Submodule.mem_iSup_of_directed
 
 /- warning: submodule.mem_Sup_of_directed -> Submodule.mem_sSup_of_directed is a dubious translation:
@@ -622,11 +617,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (HAdd.hAdd.{u2, u2, u2} (Set.{u2} M) (Set.{u2} M) (Set.{u2} M) (instHAdd.{u2} (Set.{u2} M) (Set.add.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) p'))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_sup Submodule.coe_supₓ'. -/
-theorem coe_sup : ↑(p ⊔ p') = (p + p' : Set M) :=
-  by
-  ext
-  rw [SetLike.mem_coe, mem_sup, Set.mem_add]
-  simp
+theorem coe_sup : ↑(p ⊔ p') = (p + p' : Set M) := by ext;
+  rw [SetLike.mem_coe, mem_sup, Set.mem_add]; simp
 #align submodule.coe_sup Submodule.coe_sup
 
 /- warning: submodule.sup_to_add_submonoid -> Submodule.sup_toAddSubmonoid is a dubious translation:
@@ -682,8 +674,7 @@ theorem nontrivial_span_singleton {x : M} (h : x ≠ 0) : Nontrivial (R ∙ x) :
 theorem mem_span_singleton {y : M} : (x ∈ R ∙ y) ↔ ∃ a : R, a • y = x :=
   ⟨fun h => by
     apply span_induction h
-    · rintro y (rfl | ⟨⟨⟩⟩)
-      exact ⟨1, by simp⟩
+    · rintro y (rfl | ⟨⟨⟩⟩); exact ⟨1, by simp⟩
     · exact ⟨0, by simp⟩
     · rintro _ _ ⟨a, rfl⟩ ⟨b, rfl⟩
       exact ⟨a + b, by simp [add_smul]⟩
@@ -711,10 +702,8 @@ lean 3 declaration is
 but is expected to have type
   forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (x : M), Iff (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)) (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.instTopSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (forall (v : M), Exists.{succ u1} R (fun (r : R) => Eq.{succ u2} M (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) r x) v))
 Case conversion may be inaccurate. Consider using '#align submodule.span_singleton_eq_top_iff Submodule.span_singleton_eq_top_iffₓ'. -/
-theorem span_singleton_eq_top_iff (x : M) : (R ∙ x) = ⊤ ↔ ∀ v, ∃ r : R, r • x = v :=
-  by
-  rw [eq_top_iff, le_span_singleton_iff]
-  tauto
+theorem span_singleton_eq_top_iff (x : M) : (R ∙ x) = ⊤ ↔ ∀ v, ∃ r : R, r • x = v := by
+  rw [eq_top_iff, le_span_singleton_iff]; tauto
 #align submodule.span_singleton_eq_top_iff Submodule.span_singleton_eq_top_iff
 
 /- warning: submodule.span_zero_singleton -> Submodule.span_zero_singleton is a dubious translation:
@@ -724,10 +713,7 @@ but is expected to have type
   forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))) (Bot.bot.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.instBotSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3))
 Case conversion may be inaccurate. Consider using '#align submodule.span_zero_singleton Submodule.span_zero_singletonₓ'. -/
 @[simp]
-theorem span_zero_singleton : (R ∙ (0 : M)) = ⊥ :=
-  by
-  ext
-  simp [mem_span_singleton, eq_comm]
+theorem span_zero_singleton : (R ∙ (0 : M)) = ⊥ := by ext; simp [mem_span_singleton, eq_comm]
 #align submodule.span_zero_singleton Submodule.span_zero_singleton
 
 #print Submodule.span_singleton_eq_range /-
@@ -953,23 +939,11 @@ theorem span_singleton_eq_span_singleton {R M : Type _} [Ring R] [AddCommGroup M
     exact ⟨fun hx => ⟨1, by rw [hx, smul_zero]⟩, fun ⟨z, hz⟩ => (smul_eq_zero_iff_eq z).mp hz⟩
   constructor
   · intro hxy
-    cases'
-      mem_span_singleton.mp
-        (by
-          rw [hxy]
-          apply mem_span_singleton_self) with
-      v hv
-    cases'
-      mem_span_singleton.mp
-        (by
-          rw [← hxy]
-          apply mem_span_singleton_self) with
-      i hi
-    have vi : v * i = 1 := by
-      rw [← one_smul R y, ← hi, smul_smul] at hv
+    cases' mem_span_singleton.mp (by rw [hxy]; apply mem_span_singleton_self) with v hv
+    cases' mem_span_singleton.mp (by rw [← hxy]; apply mem_span_singleton_self) with i hi
+    have vi : v * i = 1 := by rw [← one_smul R y, ← hi, smul_smul] at hv;
       exact smul_left_injective R hy hv
-    have iv : i * v = 1 := by
-      rw [← one_smul R x, ← hv, smul_smul] at hi
+    have iv : i * v = 1 := by rw [← one_smul R x, ← hv, smul_smul] at hi;
       exact smul_left_injective R hx hi
     exact ⟨⟨v, i, vi, iv⟩, hv⟩
   · rintro ⟨v, rfl⟩
@@ -1160,14 +1134,10 @@ theorem submodule_eq_sSup_le_nonzero_spans (p : Submodule R M) :
   by
   let S := { T : Submodule R M | ∃ (m : M)(hm : m ∈ p)(hz : m ≠ 0), T = span R {m} }
   apply le_antisymm
-  · intro m hm
-    by_cases h : m = 0
-    · rw [h]
-      simp
+  · intro m hm; by_cases h : m = 0
+    · rw [h]; simp
     · exact @le_sSup _ _ S _ ⟨m, ⟨hm, ⟨h, rfl⟩⟩⟩ m (mem_span_singleton_self m)
-  · rw [sSup_le_iff]
-    rintro S ⟨_, ⟨_, ⟨_, rfl⟩⟩⟩
-    rwa [span_singleton_le_iff_mem]
+  · rw [sSup_le_iff]; rintro S ⟨_, ⟨_, ⟨_, rfl⟩⟩⟩; rwa [span_singleton_le_iff_mem]
 #align submodule.submodule_eq_Sup_le_nonzero_spans Submodule.submodule_eq_sSup_le_nonzero_spans
 
 /- warning: submodule.lt_sup_iff_not_mem -> Submodule.lt_sup_iff_not_mem is a dubious translation:
@@ -1189,13 +1159,10 @@ theorem lt_sup_iff_not_mem {I : Submodule R M} {a : M} : (I < I ⊔ R ∙ a) ↔
     have h2 := gt_of_ge_of_gt h1 h
     exact lt_irrefl I h2
   · intro h
-    apply set_like.lt_iff_le_and_exists.mpr
-    constructor
+    apply set_like.lt_iff_le_and_exists.mpr; constructor
     simp only [le_sup_left]
     use a
-    constructor
-    swap
-    · assumption
+    constructor; swap; · assumption
     · have : (R ∙ a) ≤ I ⊔ R ∙ a := le_sup_right
       exact this (mem_span_singleton_self a)
 #align submodule.lt_sup_iff_not_mem Submodule.lt_sup_iff_not_mem
@@ -1228,8 +1195,7 @@ theorem mem_span_finite_of_mem_span {S : Set M} {x : M} (hx : x ∈ span R S) :
     · rwa [Finset.coe_singleton, Set.singleton_subset_iff]
     · rw [Finset.coe_singleton]
       exact Submodule.mem_span_singleton_self x
-  · use ∅
-    simp
+  · use ∅; simp
   · rintro x y ⟨X, hX, hxX⟩ ⟨Y, hY, hyY⟩
     refine' ⟨X ∪ Y, _, _⟩
     · rw [Finset.coe_union]
@@ -1379,10 +1345,8 @@ theorem mem_span_insert' {x y} {s : Set M} :
     x ∈ span R (insert y s) ↔ ∃ a : R, x + a • y ∈ span R s :=
   by
   rw [mem_span_insert]; constructor
-  · rintro ⟨a, z, hz, rfl⟩
-    exact ⟨-a, by simp [hz, add_assoc]⟩
-  · rintro ⟨a, h⟩
-    exact ⟨-a, _, h, by simp [add_comm, add_left_comm]⟩
+  · rintro ⟨a, z, hz, rfl⟩; exact ⟨-a, by simp [hz, add_assoc]⟩
+  · rintro ⟨a, h⟩; exact ⟨-a, _, h, by simp [add_comm, add_left_comm]⟩
 #align submodule.mem_span_insert' Submodule.mem_span_insert'
 
 instance : IsModularLattice (Submodule R M) :=
@@ -1498,9 +1462,7 @@ def toSpanSingleton (x : M) : R →ₗ[R] M :=
 #print LinearMap.span_singleton_eq_range /-
 /-- The range of `to_span_singleton x` is the span of `x`.-/
 theorem span_singleton_eq_range (x : M) : (R ∙ x) = (toSpanSingleton R M x).range :=
-  Submodule.ext fun y => by
-    refine' Iff.trans _ linear_map.mem_range.symm
-    exact mem_span_singleton
+  Submodule.ext fun y => by refine' Iff.trans _ linear_map.mem_range.symm; exact mem_span_singleton
 #align linear_map.span_singleton_eq_range LinearMap.span_singleton_eq_range
 -/
 
@@ -1522,10 +1484,7 @@ but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align linear_map.to_span_singleton_zero LinearMap.toSpanSingleton_zeroₓ'. -/
 @[simp]
-theorem toSpanSingleton_zero : toSpanSingleton R M 0 = 0 :=
-  by
-  ext
-  simp
+theorem toSpanSingleton_zero : toSpanSingleton R M 0 = 0 := by ext; simp
 #align linear_map.to_span_singleton_zero LinearMap.toSpanSingleton_zero
 
 end

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

@@ -138,10 +138,7 @@ theorem span_coe_eq_restrictScalars [Semiring S] [SMul S R] [Module S M] [IsScal
 #align submodule.span_coe_eq_restrict_scalars Submodule.span_coe_eq_restrictScalars
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map_span Submodule.map_spanₓ'. -/
 theorem map_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (s : Set M) :
     (span R s).map f = span R₂ (f '' s) :=
@@ -151,19 +148,13 @@ theorem map_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (
 #align submodule.map_span Submodule.map_span
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.map_span LinearMap.map_spanₓ'. -/
 alias Submodule.map_span ← _root_.linear_map.map_span
 #align linear_map.map_span LinearMap.map_span
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map_span_le Submodule.map_span_leₓ'. -/
 theorem map_span_le [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (s : Set M) (N : Submodule R₂ M₂) :
     map f (span R s) ≤ N ↔ ∀ m ∈ s, f m ∈ N :=
@@ -173,10 +164,7 @@ theorem map_span_le [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂
 #align submodule.map_span_le Submodule.map_span_le
 
 /- warning: linear_map.map_span_le -> LinearMap.map_span_le is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_map.map_span_le LinearMap.map_span_leₓ'. -/
 alias Submodule.map_span_le ← _root_.linear_map.map_span_le
 #align linear_map.map_span_le LinearMap.map_span_le
@@ -196,10 +184,7 @@ theorem span_insert_zero : span R (insert (0 : M) s) = span R s :=
 #align submodule.span_insert_zero Submodule.span_insert_zero
 
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 Case conversion may be inaccurate. Consider using '#align submodule.span_preimage_le Submodule.span_preimage_leₓ'. -/
 -- See also `span_preimage_eq` below.
 theorem span_preimage_le (f : M →ₛₗ[σ₁₂] M₂) (s : Set M₂) :
@@ -210,10 +195,7 @@ theorem span_preimage_le (f : M →ₛₗ[σ₁₂] M₂) (s : Set M₂) :
 #align submodule.span_preimage_le Submodule.span_preimage_le
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.span_preimage_le LinearMap.span_preimage_leₓ'. -/
 alias Submodule.span_preimage_le ← _root_.linear_map.span_preimage_le
 #align linear_map.span_preimage_le LinearMap.span_preimage_le
@@ -626,10 +608,7 @@ theorem mem_sup : x ∈ p ⊔ p' ↔ ∃ y ∈ p, ∃ z ∈ p', y + z = x :=
 #align submodule.mem_sup Submodule.mem_sup
 
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 Case conversion may be inaccurate. Consider using '#align submodule.mem_sup' Submodule.mem_sup'ₓ'. -/
 theorem mem_sup' : x ∈ p ⊔ p' ↔ ∃ (y : p)(z : p'), (y : M) + z = x :=
   mem_sup.trans <| by simp only [SetLike.exists, coe_mk]
@@ -998,10 +977,7 @@ theorem span_singleton_eq_span_singleton {R M : Type _} [Ring R] [AddCommGroup M
 #align submodule.span_singleton_eq_span_singleton Submodule.span_singleton_eq_span_singleton
 
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 Case conversion may be inaccurate. Consider using '#align submodule.span_image Submodule.span_imageₓ'. -/
 @[simp]
 theorem span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) :
@@ -1010,10 +986,7 @@ theorem span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂)
 #align submodule.span_image Submodule.span_image
 
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 Case conversion may be inaccurate. Consider using '#align submodule.apply_mem_span_image_of_mem_span Submodule.apply_mem_span_image_of_mem_spanₓ'. -/
 theorem apply_mem_span_image_of_mem_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) {x : M}
     {s : Set M} (h : x ∈ Submodule.span R s) : f x ∈ Submodule.span R₂ (f '' s) :=
@@ -1023,10 +996,7 @@ theorem apply_mem_span_image_of_mem_span [RingHomSurjective σ₁₂] (f : M →
 #align submodule.apply_mem_span_image_of_mem_span Submodule.apply_mem_span_image_of_mem_span
 
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 Case conversion may be inaccurate. Consider using '#align submodule.map_subtype_span_singleton Submodule.map_subtype_span_singletonₓ'. -/
 @[simp]
 theorem map_subtype_span_singleton {p : Submodule R M} (x : p) :
@@ -1034,10 +1004,7 @@ theorem map_subtype_span_singleton {p : Submodule R M} (x : p) :
 #align submodule.map_subtype_span_singleton Submodule.map_subtype_span_singleton
 
 /- warning: submodule.not_mem_span_of_apply_not_mem_span_image -> Submodule.not_mem_span_of_apply_not_mem_span_image is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.not_mem_span_of_apply_not_mem_span_image Submodule.not_mem_span_of_apply_not_mem_span_imageₓ'. -/
 /-- `f` is an explicit argument so we can `apply` this theorem and obtain `h` as a new goal. -/
 theorem not_mem_span_of_apply_not_mem_span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) {x : M}
@@ -1112,10 +1079,7 @@ theorem iSup_induction {ι : Sort _} (p : ι → Submodule R M) {C : M → Prop}
 #align submodule.supr_induction Submodule.iSup_induction
 
 /- warning: submodule.supr_induction' -> Submodule.iSup_induction' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.supr_induction' Submodule.iSup_induction'ₓ'. -/
 /-- A dependent version of `submodule.supr_induction`. -/
 @[elab_as_elim]
@@ -1352,10 +1316,7 @@ theorem prod_bot : (prod ⊥ ⊥ : Submodule R (M × M')) = ⊥ := by ext ⟨x,
 #align submodule.prod_bot Submodule.prod_bot
 
 /- warning: submodule.prod_mono -> Submodule.prod_mono is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.prod_mono Submodule.prod_monoₓ'. -/
 theorem prod_mono {p p' : Submodule R M} {q q' : Submodule R M'} :
     p ≤ p' → q ≤ q' → prod p q ≤ prod p' q' :=
@@ -1374,10 +1335,7 @@ theorem prod_inf_prod : prod p q₁ ⊓ prod p' q₁' = prod (p ⊓ p') (q₁ 
 #align submodule.prod_inf_prod Submodule.prod_inf_prod
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.prod_sup_prod Submodule.prod_sup_prodₓ'. -/
 @[simp]
 theorem prod_sup_prod : prod p q₁ ⊔ prod p' q₁' = prod (p ⊔ p') (q₁ ⊔ q₁') :=
@@ -1451,10 +1409,7 @@ variable {F : Type _} [sc : SemilinearMapClass F τ₁₂ M M₂]
 include sc
 
 /- warning: submodule.comap_map_eq -> Submodule.comap_map_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.comap_map_eq Submodule.comap_map_eqₓ'. -/
 theorem comap_map_eq (f : F) (p : Submodule R M) : comap f (map f p) = p ⊔ LinearMap.ker f :=
   by
@@ -1464,10 +1419,7 @@ theorem comap_map_eq (f : F) (p : Submodule R M) : comap f (map f p) = p ⊔ Lin
 #align submodule.comap_map_eq Submodule.comap_map_eq
 
 /- warning: submodule.comap_map_eq_self -> Submodule.comap_map_eq_self is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.comap_map_eq_self Submodule.comap_map_eq_selfₓ'. -/
 theorem comap_map_eq_self {f : F} {p : Submodule R M} (h : LinearMap.ker f ≤ p) :
     comap f (map f p) = p := by rw [Submodule.comap_map_eq, sup_of_le_left h]
@@ -1500,40 +1452,28 @@ include R
 include sc
 
 /- warning: linear_map.map_le_map_iff -> LinearMap.map_le_map_iff is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.map_le_map_iff LinearMap.map_le_map_iffₓ'. -/
 protected theorem map_le_map_iff (f : F) {p p'} : map f p ≤ map f p' ↔ p ≤ p' ⊔ ker f := by
   rw [map_le_iff_le_comap, Submodule.comap_map_eq]
 #align linear_map.map_le_map_iff LinearMap.map_le_map_iff
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.map_le_map_iff' LinearMap.map_le_map_iff'ₓ'. -/
 theorem map_le_map_iff' {f : F} (hf : ker f = ⊥) {p p'} : map f p ≤ map f p' ↔ p ≤ p' := by
   rw [LinearMap.map_le_map_iff, hf, sup_bot_eq]
 #align linear_map.map_le_map_iff' LinearMap.map_le_map_iff'
 
 /- warning: linear_map.map_injective -> LinearMap.map_injective is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_map.map_injective LinearMap.map_injectiveₓ'. -/
 theorem map_injective {f : F} (hf : ker f = ⊥) : Injective (map f) := fun p p' h =>
   le_antisymm ((map_le_map_iff' hf).1 (le_of_eq h)) ((map_le_map_iff' hf).1 (ge_of_eq h))
 #align linear_map.map_injective LinearMap.map_injective
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.map_eq_top_iff LinearMap.map_eq_top_iffₓ'. -/
 theorem map_eq_top_iff {f : F} (hf : range f = ⊤) {p : Submodule R M} :
     p.map f = ⊤ ↔ p ⊔ LinearMap.ker f = ⊤ := by
@@ -1599,10 +1539,7 @@ variable [Semiring R₂] [AddCommMonoid M₂] [Module R₂ M₂]
 variable {σ₁₂ : R →+* R₂}
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.eq_on_span LinearMap.eqOn_spanₓ'. -/
 /-- If two linear maps are equal on a set `s`, then they are equal on `submodule.span s`.
 
@@ -1612,10 +1549,7 @@ theorem eqOn_span {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (H : Set.EqOn f
 #align linear_map.eq_on_span LinearMap.eqOn_span
 
 /- warning: linear_map.eq_on_span' -> LinearMap.eqOn_span' is a dubious translation:
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 /-- If two linear maps are equal on a set `s`, then they are equal on `submodule.span s`.
 
@@ -1627,10 +1561,7 @@ theorem eqOn_span' {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (H : Set.EqOn
 #align linear_map.eq_on_span' LinearMap.eqOn_span'
 
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 /-- If `s` generates the whole module and linear maps `f`, `g` are equal on `s`, then they are
 equal. -/
@@ -1639,10 +1570,7 @@ theorem ext_on {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (hv : span R s = 
 #align linear_map.ext_on LinearMap.ext_on
 
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 /-- If the range of `v : ι → M` generates the whole module and linear maps `f`, `g` are equal at
 each `v i`, then they are equal. -/
@@ -1678,10 +1606,7 @@ noncomputable section
 open Classical
 
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(Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))
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_inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) {x : V}, (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => K) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (LinearMap.semilinearMapClass.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f)) (Top.top.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.span_singleton_sup_ker_eq_top LinearMap.span_singleton_sup_ker_eq_topₓ'. -/
 theorem span_singleton_sup_ker_eq_top (f : V →ₗ[K] K) {x : V} (hx : f x ≠ 0) :
     (K ∙ x) ⊔ f.ker = ⊤ :=
@@ -1720,10 +1645,7 @@ def toSpanNonzeroSingleton : R ≃ₗ[R] R ∙ x :=
 #align linear_equiv.to_span_nonzero_singleton LinearEquiv.toSpanNonzeroSingleton
 
 /- warning: linear_equiv.to_span_nonzero_singleton_one -> LinearEquiv.toSpanNonzeroSingleton_one is a dubious translation:
-lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) a) (SMulHomClass.toFunLike.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Module.toDistribMulAction.{u1, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (LinearEquiv.{u1, u1, u1, u2} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R 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(Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) 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(Set.instSingletonSet.{u2} M) _inst_4)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 x) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Subtype.mk.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) _inst_4 (Submodule.mem_span_singleton_self.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_4))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_equiv.to_span_nonzero_singleton_one LinearEquiv.toSpanNonzeroSingleton_oneₓ'. -/
 theorem toSpanNonzeroSingleton_one :
     LinearEquiv.toSpanNonzeroSingleton R M x h 1 =
@@ -1747,10 +1669,7 @@ abbrev coord : (R ∙ x) ≃ₗ[R] R :=
 #align linear_equiv.coord LinearEquiv.coord
 
 /- warning: linear_equiv.coord_self -> LinearEquiv.coord_self is a dubious translation:
-lean 3 declaration is
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(Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) => R) a) (SMulHomClass.toFunLike.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R (SMulZeroClass.toSMul.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Module.toDistribMulAction.{u1, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u1, max u1 u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R (LinearEquiv.{u1, u1, u2, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u1} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_equiv.coord_self LinearEquiv.coord_selfₓ'. -/
 theorem coord_self : (coord R M x h) (⟨x, Submodule.mem_span_singleton_self x⟩ : R ∙ x) = 1 := by
   rw [← to_span_nonzero_singleton_one R M x h, LinearEquiv.symm_apply_apply]

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

@@ -5,7 +5,7 @@ Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Fréd
   Heather Macbeth
 
 ! This file was ported from Lean 3 source module linear_algebra.span
-! leanprover-community/mathlib commit 1ead22342e1a078bd44744ace999f85756555d35
+! leanprover-community/mathlib commit 10878f6bf1dab863445907ab23fbfcefcb5845d0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1653,6 +1653,22 @@ theorem ext_on_range {ι : Type _} {v : ι → M} {f g : M →ₛₗ[σ₁₂] M
 
 end AddCommMonoid
 
+section NoZeroDivisors
+
+variable (R M) [Ring R] [AddCommGroup M] [Module R M] [NoZeroSMulDivisors R M]
+
+/- warning: linear_map.ker_to_span_singleton -> LinearMap.ker_toSpanSingleton is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_map.ker_to_span_singleton LinearMap.ker_toSpanSingletonₓ'. -/
+theorem ker_toSpanSingleton {x : M} (h : x ≠ 0) : (toSpanSingleton R M x).ker = ⊥ :=
+  SetLike.ext fun c => smul_eq_zero.trans <| or_iff_left_of_imp fun h' => (h h').elim
+#align linear_map.ker_to_span_singleton LinearMap.ker_toSpanSingleton
+
+end NoZeroDivisors
+
 section Field
 
 variable {K V} [Field K] [AddCommGroup V] [Module K V]
@@ -1678,34 +1694,6 @@ theorem span_singleton_sup_ker_eq_top (f : V →ₗ[K] K) {x : V} (hx : f x ≠
           by simp only [add_sub_cancel'_right]⟩⟩
 #align linear_map.span_singleton_sup_ker_eq_top LinearMap.span_singleton_sup_ker_eq_top
 
-variable (K V)
-
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(Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) K V (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u1, u2} K K K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.toSpanSingleton.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x)) (Bot.bot.{u1} (Submodule.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Submodule.instBotSubmodule.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))
-Case conversion may be inaccurate. Consider using '#align linear_map.ker_to_span_singleton LinearMap.ker_toSpanSingletonₓ'. -/
-theorem ker_toSpanSingleton {x : V} (h : x ≠ 0) : (toSpanSingleton K V x).ker = ⊥ :=
-  by
-  ext c; constructor
-  · intro hc
-    rw [Submodule.mem_bot]
-    rw [mem_ker] at hc
-    by_contra hc'
-    have : x = 0
-    calc
-      x = c⁻¹ • c • x := by rw [← mul_smul, inv_mul_cancel hc', one_smul]
-      _ = c⁻¹ • (to_span_singleton K V x) c := rfl
-      _ = 0 := by rw [hc, smul_zero]
-      
-    tauto
-  · rw [mem_ker, Submodule.mem_bot]
-    intro h
-    rw [h]
-    simp
-#align linear_map.ker_to_span_singleton LinearMap.ker_toSpanSingleton
-
 end Field
 
 end LinearMap
@@ -1714,65 +1702,63 @@ open LinearMap
 
 namespace LinearEquiv
 
-section Field
-
-variable (K V) [Field K] [AddCommGroup V] [Module K V]
+variable (R M) [Ring R] [AddCommGroup M] [Module R M] [NoZeroSMulDivisors R M] (x : M) (h : x ≠ 0)
 
 /- warning: linear_equiv.to_span_nonzero_singleton -> LinearEquiv.toSpanNonzeroSingleton is a dubious translation:
 lean 3 declaration is
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (LinearEquiv.{u1, u1, u1, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} K _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} K _inst_1) K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))))
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : NoZeroSMulDivisors.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{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 (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))] (x : M), (Ne.{succ u2} M x (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))))))))) -> (LinearEquiv.{u1, u1, u1, 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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} R _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} R _inst_1) R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Field.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (_inst_4 : M), (Ne.{succ u2} M _inst_4 (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2)))))))) -> (LinearEquiv.{u1, u1, u1, u2} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.to_span_nonzero_singleton LinearEquiv.toSpanNonzeroSingletonₓ'. -/
-/-- Given a nonzero element `x` of a vector space `V` over a field `K`, the natural
-    map from `K` to the span of `x`, with invertibility check to consider it as an
-    isomorphism.-/
-def toSpanNonzeroSingleton (x : V) (h : x ≠ 0) : K ≃ₗ[K] K ∙ x :=
+/-- Given a nonzero element `x` of a torsion-free module `M` over a ring `R`, the natural
+isomorphism from `R` to the span of `x` given by $r \mapsto r \cdot x$. -/
+def toSpanNonzeroSingleton : R ≃ₗ[R] R ∙ x :=
   LinearEquiv.trans
-    (LinearEquiv.ofInjective (LinearMap.toSpanSingleton K V x)
-      (ker_eq_bot.1 <| LinearMap.ker_toSpanSingleton K V h))
-    (LinearEquiv.ofEq (toSpanSingleton K V x).range (K ∙ x) (span_singleton_eq_range K V x).symm)
+    (LinearEquiv.ofInjective (LinearMap.toSpanSingleton R M x)
+      (ker_eq_bot.1 <| ker_toSpanSingleton R M h))
+    (LinearEquiv.ofEq (toSpanSingleton R M x).range (R ∙ x) (span_singleton_eq_range R M x).symm)
 #align linear_equiv.to_span_nonzero_singleton LinearEquiv.toSpanNonzeroSingleton
 
 /- warning: linear_equiv.to_span_nonzero_singleton_one -> LinearEquiv.toSpanNonzeroSingleton_one is a dubious translation:
 lean 3 declaration is
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K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)))) => K -> (coeSort.{succ u2, succ (succ u2)} 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(Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} K _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} K _inst_1)) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.Mem.{u2, u2} V (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : NoZeroSMulDivisors.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{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 (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))] (x : M) (h : Ne.{succ u2} M x (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))))))))), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, u1, 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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} R _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} R _inst_1) R (coeSort.{succ 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_inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x)))) (fun (_x : LinearEquiv.{u1, u1, u1, 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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} R _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} R _inst_1) R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x)))) => R -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x)))) (LinearEquiv.hasCoeToFun.{u1, u1, u1, u2} R R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) (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))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} R _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} R _inst_1)) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 x h) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))))) (Subtype.mk.{succ u2} M (fun (x_1 : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) x (Submodule.mem_span_singleton_self.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 x))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u2, max u1 u2} K K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u2} K K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Field.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (_inst_4 : M) (x : Ne.{succ u2} M _inst_4 (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2)))))))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : R) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearEquiv.{u1, u1, u1, u2} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : R) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) a) (SMulHomClass.toFunLike.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Module.toDistribMulAction.{u1, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (LinearEquiv.{u1, u1, u1, u2} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u2, max u1 u2} R R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (LinearEquiv.{u1, u1, u1, u2} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u2} R R R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))))) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 x) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))))) (Subtype.mk.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) _inst_4 (Submodule.mem_span_singleton_self.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_4))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.to_span_nonzero_singleton_one LinearEquiv.toSpanNonzeroSingleton_oneₓ'. -/
-theorem toSpanNonzeroSingleton_one (x : V) (h : x ≠ 0) :
-    LinearEquiv.toSpanNonzeroSingleton K V x h 1 =
-      (⟨x, Submodule.mem_span_singleton_self x⟩ : K ∙ x) :=
+theorem toSpanNonzeroSingleton_one :
+    LinearEquiv.toSpanNonzeroSingleton R M x h 1 =
+      (⟨x, Submodule.mem_span_singleton_self x⟩ : R ∙ x) :=
   by
   apply set_like.coe_eq_coe.mp
-  have : ↑(to_span_nonzero_singleton K V x h 1) = to_span_singleton K V x 1 := rfl
+  have : ↑(to_span_nonzero_singleton R M x h 1) = to_span_singleton R M x 1 := rfl
   rw [this, to_span_singleton_one, Submodule.coe_mk]
 #align linear_equiv.to_span_nonzero_singleton_one LinearEquiv.toSpanNonzeroSingleton_one
 
 /- warning: linear_equiv.coord -> LinearEquiv.coord is a dubious translation:
 lean 3 declaration is
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) K (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : NoZeroSMulDivisors.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{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 (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))] (x : M), (Ne.{succ u2} M x (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))))))))) -> (LinearEquiv.{u1, u1, u2, 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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearEquiv.coord._proof_1.{u1} R _inst_1) (LinearEquiv.coord._proof_2.{u1} R _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) R (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{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_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Field.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (_inst_4 : M), (Ne.{succ u2} M _inst_4 (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2)))))))) -> (LinearEquiv.{u1, u1, u2, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.coord LinearEquiv.coordₓ'. -/
-/-- Given a nonzero element `x` of a vector space `V` over a field `K`, the natural map
-    from the span of `x` to `K`.-/
-abbrev coord (x : V) (h : x ≠ 0) : (K ∙ x) ≃ₗ[K] K :=
-  (toSpanNonzeroSingleton K V x h).symm
+/-- Given a nonzero element `x` of a torsion-free module `M` over a ring `R`, the natural
+isomorphism from the span of `x` to `R` given by $r \cdot x \mapsto r$. -/
+abbrev coord : (R ∙ x) ≃ₗ[R] R :=
+  (toSpanNonzeroSingleton R M x h).symm
 #align linear_equiv.coord LinearEquiv.coord
 
 /- warning: linear_equiv.coord_self -> LinearEquiv.coord_self is a dubious translation:
 lean 3 declaration is
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(Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 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(Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))] (x : M) (h : Ne.{succ u2} M x (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2))))))))), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearEquiv.{u1, u1, u2, u1} R R 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(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_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{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_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) (Semiring.toModule.{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))) (LinearEquiv.coord._proof_1.{u1} R _inst_1) (LinearEquiv.coord._proof_2.{u1} R _inst_1)) (LinearEquiv.coord.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 x h) (Subtype.mk.{succ u2} M (fun (x_1 : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))) x (Submodule.mem_span_singleton_self.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 x))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R _inst_1)))))))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (fun (_x : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u1, max u1 u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u1, max u1 u2} K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} 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K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) _inst_1))))))
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Field.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (_inst_4 : M) (x : Ne.{succ u2} M _inst_4 (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (NegZeroClass.toZero.{u2} M (SubNegZeroMonoid.toNegZeroClass.{u2} M (SubtractionMonoid.toSubNegZeroMonoid.{u2} M (SubtractionCommMonoid.toSubtractionMonoid.{u2} M (AddCommGroup.toDivisionAddCommMonoid.{u2} M _inst_2)))))))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) => R) (Subtype.mk.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) _inst_4 (Submodule.mem_span_singleton_self.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (LinearEquiv.{u1, u1, u2, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (fun (a : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) => R) a) (SMulHomClass.toFunLike.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R (SMulZeroClass.toSMul.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))))) (DistribMulAction.toDistribSMul.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))))))) (SMulZeroClass.toSMul.{u1, u1} R R (AddMonoid.toZero.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R R (AddMonoid.toAddZeroClass.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) (Module.toDistribMulAction.{u1, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u1, max u1 u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R (LinearEquiv.{u1, u1, u2, u1} R R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1)))) (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) R (Submodule.addCommMonoid.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (DivisionRing.toRing.{u1} R (Field.toDivisionRing.{u1} R _inst_1)))))) (Submodule.module.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) (Semiring.toModule.{u1} R (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))))) (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) 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_inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) => R) (Subtype.mk.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) _inst_4 (Submodule.mem_span_singleton_self.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_4))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) => R) (Subtype.mk.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) _inst_4 (Submodule.mem_span_singleton_self.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_4))) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) => R) (Subtype.mk.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) _inst_4 (Submodule.mem_span_singleton_self.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_4))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) => R) (Subtype.mk.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) _inst_4 (Submodule.mem_span_singleton_self.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_4))) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) => R) (Subtype.mk.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4))) _inst_4 (Submodule.mem_span_singleton_self.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_4))) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) _inst_4)))) => R) (Subtype.mk.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R (Semifield.toDivisionSemiring.{u1} R (Field.toSemifield.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (DivisionSemiring.toSemiring.{u1} R 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 Case conversion may be inaccurate. Consider using '#align linear_equiv.coord_self LinearEquiv.coord_selfₓ'. -/
-theorem coord_self (x : V) (h : x ≠ 0) :
-    (coord K V x h) (⟨x, Submodule.mem_span_singleton_self x⟩ : K ∙ x) = 1 := by
-  rw [← to_span_nonzero_singleton_one K V x h, LinearEquiv.symm_apply_apply]
+theorem coord_self : (coord R M x h) (⟨x, Submodule.mem_span_singleton_self x⟩ : R ∙ x) = 1 := by
+  rw [← to_span_nonzero_singleton_one R M x h, LinearEquiv.symm_apply_apply]
 #align linear_equiv.coord_self LinearEquiv.coord_self
 
-end Field
+theorem coord_apply_smul (y : Submodule.span R ({x} : Set M)) : coord R M x h y • x = y :=
+  Subtype.ext_iff.1 <| (toSpanNonzeroSingleton R M x h).apply_symm_apply _
+#align linear_equiv.coord_apply_smul LinearEquiv.coord_apply_smul
 
 end LinearEquiv
 

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

@@ -141,7 +141,7 @@ theorem span_coe_eq_restrictScalars [Semiring S] [SMul S R] [Module S M] [IsScal
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u3} M), Eq.{succ u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s))
 Case conversion may be inaccurate. Consider using '#align submodule.map_span Submodule.map_spanₓ'. -/
 theorem map_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (s : Set M) :
     (span R s).map f = span R₂ (f '' s) :=
@@ -154,7 +154,7 @@ theorem map_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u3} M), Eq.{succ u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s))
 Case conversion may be inaccurate. Consider using '#align linear_map.map_span LinearMap.map_spanₓ'. -/
 alias Submodule.map_span ← _root_.linear_map.map_span
 #align linear_map.map_span LinearMap.map_span
@@ -163,7 +163,7 @@ alias Submodule.map_span ← _root_.linear_map.map_span
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u3} M) (N : Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toHasLe.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)))) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) m s) -> (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M) (N : Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) m s) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) m) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M) (N : Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) m s) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) m) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 Case conversion may be inaccurate. Consider using '#align submodule.map_span_le Submodule.map_span_leₓ'. -/
 theorem map_span_le [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (s : Set M) (N : Submodule R₂ M₂) :
     map f (span R s) ≤ N ↔ ∀ m ∈ s, f m ∈ N :=
@@ -176,7 +176,7 @@ theorem map_span_le [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u3} M) (N : Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toHasLe.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)))) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) m s) -> (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M) (N : Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) m s) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) m) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M) (N : Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) m s) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) m) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 Case conversion may be inaccurate. Consider using '#align linear_map.map_span_le LinearMap.map_span_leₓ'. -/
 alias Submodule.map_span_le ← _root_.linear_map.map_span_le
 #align linear_map.map_span_le LinearMap.map_span_le
@@ -199,7 +199,7 @@ theorem span_insert_zero : span R (insert (0 : M) s) = span R s :=
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u4} M₂), LE.le.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u1} M₂), LE.le.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u4, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u1} M₂), LE.le.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u4, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
 Case conversion may be inaccurate. Consider using '#align submodule.span_preimage_le Submodule.span_preimage_leₓ'. -/
 -- See also `span_preimage_eq` below.
 theorem span_preimage_le (f : M →ₛₗ[σ₁₂] M₂) (s : Set M₂) :
@@ -213,7 +213,7 @@ theorem span_preimage_le (f : M →ₛₗ[σ₁₂] M₂) (s : Set M₂) :
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u4} M₂), LE.le.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u1} M₂), LE.le.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u4, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u1} M₂), LE.le.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u4, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
 Case conversion may be inaccurate. Consider using '#align linear_map.span_preimage_le LinearMap.span_preimage_leₓ'. -/
 alias Submodule.span_preimage_le ← _root_.linear_map.span_preimage_le
 #align linear_map.span_preimage_le LinearMap.span_preimage_le
@@ -1001,7 +1001,7 @@ theorem span_singleton_eq_span_singleton {R M : Type _} [Ring R] [AddCommGroup M
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] {s : Set.{u3} M} [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6), Eq.{succ u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] {s : Set.{u2} M} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] {s : Set.{u2} M} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s))
 Case conversion may be inaccurate. Consider using '#align submodule.span_image Submodule.span_imageₓ'. -/
 @[simp]
 theorem span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) :
@@ -1013,7 +1013,7 @@ theorem span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂)
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u3} M}, (Membership.Mem.{u3, u3} M (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) -> (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u2} M}, (Membership.mem.{u2, u2} M (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u4, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u2} M}, (Membership.mem.{u2, u2} M (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u4, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))
 Case conversion may be inaccurate. Consider using '#align submodule.apply_mem_span_image_of_mem_span Submodule.apply_mem_span_image_of_mem_spanₓ'. -/
 theorem apply_mem_span_image_of_mem_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) {x : M}
     {s : Set M} (h : x ∈ Submodule.span R s) : f x ∈ Submodule.span R₂ (f '' s) :=
@@ -1037,7 +1037,7 @@ theorem map_subtype_span_singleton {p : Submodule R M} (x : p) :
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u3} M}, (Not (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))) -> (Not (Membership.Mem.{u3, u3} M (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u2} M}, (Not (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))) -> (Not (Membership.mem.{u2, u2} M (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u4, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u2} M}, (Not (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))) -> (Not (Membership.mem.{u2, u2} M (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u4, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)))
 Case conversion may be inaccurate. Consider using '#align submodule.not_mem_span_of_apply_not_mem_span_image Submodule.not_mem_span_of_apply_not_mem_span_imageₓ'. -/
 /-- `f` is an explicit argument so we can `apply` this theorem and obtain `h` as a new goal. -/
 theorem not_mem_span_of_apply_not_mem_span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) {x : M}
@@ -1568,7 +1568,7 @@ theorem span_singleton_eq_range (x : M) : (R ∙ x) = (toSpanSingleton R M x).ra
 lean 3 declaration is
   forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (x : M), Eq.{succ u2} M (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3) (fun (_x : LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3) => R -> M) (LinearMap.hasCoeToFun.{u1, u1, u1, u2} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.toSpanSingleton.{u1, u2} R M _inst_1 _inst_2 _inst_3 x) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) x
 but is expected to have type
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => M) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u2} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.toSpanSingleton.{u1, u2} R M _inst_1 _inst_2 _inst_3 x) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) x
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => M) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u2} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.toSpanSingleton.{u1, u2} R M _inst_1 _inst_2 _inst_3 x) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) x
 Case conversion may be inaccurate. Consider using '#align linear_map.to_span_singleton_one LinearMap.toSpanSingleton_oneₓ'. -/
 @[simp]
 theorem toSpanSingleton_one (x : M) : toSpanSingleton R M x 1 = x :=
@@ -1602,7 +1602,7 @@ variable {σ₁₂ : R →+* R₂}
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u3} M} {f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (forall {{x : M}}, (Membership.Mem.{u3, u3} M (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g x)))
 but is expected to have type
-  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (forall {{x : M}}, (Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u3, u4} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g x)))
+  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (forall {{x : M}}, (Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u3, u4} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g x)))
 Case conversion may be inaccurate. Consider using '#align linear_map.eq_on_span LinearMap.eqOn_spanₓ'. -/
 /-- If two linear maps are equal on a set `s`, then they are equal on `submodule.span s`.
 
@@ -1615,7 +1615,7 @@ theorem eqOn_span {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (H : Set.EqOn f
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u3} M} {f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Set.EqOn.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)))
 but is expected to have type
-  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) (SetLike.coe.{u4, u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s)))
+  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) (SetLike.coe.{u4, u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s)))
 Case conversion may be inaccurate. Consider using '#align linear_map.eq_on_span' LinearMap.eqOn_span'ₓ'. -/
 /-- If two linear maps are equal on a set `s`, then they are equal on `submodule.span s`.
 
@@ -1630,7 +1630,7 @@ theorem eqOn_span' {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (H : Set.EqOn
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u3} M} {f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Eq.{succ u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s) (Top.top.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.hasTop.{u1, u3} R M _inst_1 _inst_2 _inst_3))) -> (Set.EqOn.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Eq.{max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) f g)
 but is expected to have type
-  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Eq.{succ u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s) (Top.top.{u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.instTopSubmodule.{u3, u4} R M _inst_1 _inst_2 _inst_3))) -> (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Eq.{max (succ u4) (succ u1)} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) f g)
+  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Eq.{succ u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s) (Top.top.{u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.instTopSubmodule.{u3, u4} R M _inst_1 _inst_2 _inst_3))) -> (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Eq.{max (succ u4) (succ u1)} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) f g)
 Case conversion may be inaccurate. Consider using '#align linear_map.ext_on LinearMap.ext_onₓ'. -/
 /-- If `s` generates the whole module and linear maps `f`, `g` are equal on `s`, then they are
 equal. -/
@@ -1642,7 +1642,7 @@ theorem ext_on {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (hv : span R s = 
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {ι : Type.{u5}} {v : ι -> M} {f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Eq.{succ u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 (Set.range.{u3, succ u5} M ι v)) (Top.top.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.hasTop.{u1, u3} R M _inst_1 _inst_2 _inst_3))) -> (forall (i : ι), Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (v i)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g (v i))) -> (Eq.{max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) f g)
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} {ι : Type.{u5}} {v : ι -> M} {f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Eq.{succ u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.range.{u2, succ u5} M ι v)) (Top.top.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.instTopSubmodule.{u4, u2} R M _inst_1 _inst_2 _inst_3))) -> (forall (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) (v i)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (v i)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g (v i))) -> (Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) f g)
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} {ι : Type.{u5}} {v : ι -> M} {f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Eq.{succ u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.range.{u2, succ u5} M ι v)) (Top.top.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.instTopSubmodule.{u4, u2} R M _inst_1 _inst_2 _inst_3))) -> (forall (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) (v i)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (v i)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g (v i))) -> (Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) f g)
 Case conversion may be inaccurate. Consider using '#align linear_map.ext_on_range LinearMap.ext_on_rangeₓ'. -/
 /-- If the range of `v : ι → M` generates the whole module and linear maps `f`, `g` are equal at
 each `v i`, then they are equal. -/
@@ -1665,7 +1665,7 @@ open Classical
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (f : LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) {x : V}, (Ne.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) => V -> K) (LinearMap.hasCoeToFun.{u1, u1, u2, u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f x) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)) (LinearMap.ker.{u1, u1, u2, u1, max u2 u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.semilinearMapClass.{u1, u1, u2, u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f)) (Top.top.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))
 but is expected to have type
-  forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] (f : LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) {x : V}, (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => K) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => K) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => K) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => K) x) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => K) x) (CommGroupWithZero.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => K) x) (Semifield.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => K) x) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => K) x) _inst_1))))))) -> (Eq.{succ u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Sup.sup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Submodule.span.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3 (Singleton.singleton.{u1, u1} V (Set.{u1} V) (Set.instSingletonSet.{u1} V) x)) (LinearMap.ker.{u2, u2, u1, u2, max u2 u1} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (LinearMap.semilinearMapClass.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f)) (Top.top.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3)))
+  forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] (f : LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) {x : V}, (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => K) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => K) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => K) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => K) x) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => K) x) (CommGroupWithZero.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => K) x) (Semifield.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => K) x) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => K) x) _inst_1))))))) -> (Eq.{succ u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Sup.sup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Submodule.span.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3 (Singleton.singleton.{u1, u1} V (Set.{u1} V) (Set.instSingletonSet.{u1} V) x)) (LinearMap.ker.{u2, u2, u1, u2, max u2 u1} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (LinearMap.semilinearMapClass.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f)) (Top.top.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3)))
 Case conversion may be inaccurate. Consider using '#align linear_map.span_singleton_sup_ker_eq_top LinearMap.span_singleton_sup_ker_eq_topₓ'. -/
 theorem span_singleton_sup_ker_eq_top (f : V →ₗ[K] K) {x : V} (hx : f x ≠ 0) :
     (K ∙ x) ⊔ f.ker = ⊤ :=
@@ -1738,7 +1738,7 @@ def toSpanNonzeroSingleton (x : V) (h : x ≠ 0) : K ≃ₗ[K] K ∙ x :=
 lean 3 declaration is
   forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, u1, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) 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(AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V 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K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)))) => K -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)))) (LinearEquiv.hasCoeToFun.{u1, u1, u1, u2} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K 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(NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} K _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} K _inst_1)) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.Mem.{u2, u2} V (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u2, max u1 u2} K K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u2} K K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))
+  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u2, max u1 u2} K K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u2} K K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.to_span_nonzero_singleton_one LinearEquiv.toSpanNonzeroSingleton_oneₓ'. -/
 theorem toSpanNonzeroSingleton_one (x : V) (h : x ≠ 0) :
     LinearEquiv.toSpanNonzeroSingleton K V x h 1 =
@@ -1765,7 +1765,7 @@ abbrev coord (x : V) (h : x ≠ 0) : (K ∙ x) ≃ₗ[K] K :=
 lean 3 declaration is
   forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))), Eq.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) K (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) K (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) => (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) -> K) (LinearEquiv.hasCoeToFun.{u1, u1, u2, u1} K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1)) (LinearEquiv.coord.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.Mem.{u2, u2} V (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (fun (_x : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u1, max u1 u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u1, max u1 u2} K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) 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K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) 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(Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) _inst_1))))))
+  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (fun (_x : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u1, max u1 u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u1, max u1 u2} K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K 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_inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.coord_self LinearEquiv.coord_selfₓ'. -/
 theorem coord_self (x : V) (h : x ≠ 0) :
     (coord K V x h) (⟨x, Submodule.mem_span_singleton_self x⟩ : K ∙ x) = 1 := by

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

@@ -141,7 +141,7 @@ theorem span_coe_eq_restrictScalars [Semiring S] [SMul S R] [Module S M] [IsScal
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u3} M), Eq.{succ u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s))
 Case conversion may be inaccurate. Consider using '#align submodule.map_span Submodule.map_spanₓ'. -/
 theorem map_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (s : Set M) :
     (span R s).map f = span R₂ (f '' s) :=
@@ -154,7 +154,7 @@ theorem map_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u3} M), Eq.{succ u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s))
 Case conversion may be inaccurate. Consider using '#align linear_map.map_span LinearMap.map_spanₓ'. -/
 alias Submodule.map_span ← _root_.linear_map.map_span
 #align linear_map.map_span LinearMap.map_span
@@ -163,7 +163,7 @@ alias Submodule.map_span ← _root_.linear_map.map_span
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u3} M) (N : Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toHasLe.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)))) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) m s) -> (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M) (N : Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) m s) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) m) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M) (N : Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) m s) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) m) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 Case conversion may be inaccurate. Consider using '#align submodule.map_span_le Submodule.map_span_leₓ'. -/
 theorem map_span_le [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (s : Set M) (N : Submodule R₂ M₂) :
     map f (span R s) ≤ N ↔ ∀ m ∈ s, f m ∈ N :=
@@ -176,7 +176,7 @@ theorem map_span_le [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u3} M) (N : Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toHasLe.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)))) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) m s) -> (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M) (N : Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) m s) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) m) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M) (N : Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) m s) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) m) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 Case conversion may be inaccurate. Consider using '#align linear_map.map_span_le LinearMap.map_span_leₓ'. -/
 alias Submodule.map_span_le ← _root_.linear_map.map_span_le
 #align linear_map.map_span_le LinearMap.map_span_le
@@ -199,7 +199,7 @@ theorem span_insert_zero : span R (insert (0 : M) s) = span R s :=
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u4} M₂), LE.le.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u1} M₂), LE.le.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u4, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u1} M₂), LE.le.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u4, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
 Case conversion may be inaccurate. Consider using '#align submodule.span_preimage_le Submodule.span_preimage_leₓ'. -/
 -- See also `span_preimage_eq` below.
 theorem span_preimage_le (f : M →ₛₗ[σ₁₂] M₂) (s : Set M₂) :
@@ -213,7 +213,7 @@ theorem span_preimage_le (f : M →ₛₗ[σ₁₂] M₂) (s : Set M₂) :
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u4} M₂), LE.le.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u1} M₂), LE.le.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u4, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u1} M₂), LE.le.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u4, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
 Case conversion may be inaccurate. Consider using '#align linear_map.span_preimage_le LinearMap.span_preimage_leₓ'. -/
 alias Submodule.span_preimage_le ← _root_.linear_map.span_preimage_le
 #align linear_map.span_preimage_le LinearMap.span_preimage_le
@@ -1001,7 +1001,7 @@ theorem span_singleton_eq_span_singleton {R M : Type _} [Ring R] [AddCommGroup M
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] {s : Set.{u3} M} [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6), Eq.{succ u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] {s : Set.{u2} M} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] {s : Set.{u2} M} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s))
 Case conversion may be inaccurate. Consider using '#align submodule.span_image Submodule.span_imageₓ'. -/
 @[simp]
 theorem span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) :
@@ -1013,7 +1013,7 @@ theorem span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂)
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u3} M}, (Membership.Mem.{u3, u3} M (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) -> (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u2} M}, (Membership.mem.{u2, u2} M (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u4, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u2} M}, (Membership.mem.{u2, u2} M (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u4, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))
 Case conversion may be inaccurate. Consider using '#align submodule.apply_mem_span_image_of_mem_span Submodule.apply_mem_span_image_of_mem_spanₓ'. -/
 theorem apply_mem_span_image_of_mem_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) {x : M}
     {s : Set M} (h : x ∈ Submodule.span R s) : f x ∈ Submodule.span R₂ (f '' s) :=
@@ -1026,7 +1026,7 @@ theorem apply_mem_span_image_of_mem_span [RingHomSurjective σ₁₂] (f : M →
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.map.{u1, u1, u2, u2, u2} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_2 (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_2 (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_2 (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Submodule.subtype.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.span.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Singleton.singleton.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) (Set.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p)) (Set.hasSingleton.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p)) x))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) ((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_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p))))) x)))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {p : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3} (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)), Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.map.{u2, u2, u1, u1, u1} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) M _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_2 (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomSurjective.ids.{u2} R _inst_1) (LinearMap.{u2, u2, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) M (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_2 (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) M _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_2 (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Submodule.subtype.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.span.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Singleton.singleton.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) (Set.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p))) (Set.instSingletonSet.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p))) x))) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) (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_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) p)) x)))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {p : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3} (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)), Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.map.{u2, u2, u1, u1, u1} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) M _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_2 (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomSurjective.ids.{u2} R _inst_1) (LinearMap.{u2, u2, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) M (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_2 (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) M _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_2 (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Submodule.subtype.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.span.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Singleton.singleton.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) (Set.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p))) (Set.instSingletonSet.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p))) x))) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) (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_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) p)) x)))
 Case conversion may be inaccurate. Consider using '#align submodule.map_subtype_span_singleton Submodule.map_subtype_span_singletonₓ'. -/
 @[simp]
 theorem map_subtype_span_singleton {p : Submodule R M} (x : p) :
@@ -1037,7 +1037,7 @@ theorem map_subtype_span_singleton {p : Submodule R M} (x : p) :
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u3} M}, (Not (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))) -> (Not (Membership.Mem.{u3, u3} M (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u2} M}, (Not (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))) -> (Not (Membership.mem.{u2, u2} M (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u4, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u2} M}, (Not (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))) -> (Not (Membership.mem.{u2, u2} M (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u4, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)))
 Case conversion may be inaccurate. Consider using '#align submodule.not_mem_span_of_apply_not_mem_span_image Submodule.not_mem_span_of_apply_not_mem_span_imageₓ'. -/
 /-- `f` is an explicit argument so we can `apply` this theorem and obtain `h` as a new goal. -/
 theorem not_mem_span_of_apply_not_mem_span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) {x : M}
@@ -1555,24 +1555,20 @@ def toSpanSingleton (x : M) : R →ₗ[R] M :=
 #align linear_map.to_span_singleton LinearMap.toSpanSingleton
 -/
 
-/- warning: linear_map.span_singleton_eq_range -> LinearMap.span_singleton_eq_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_map.span_singleton_eq_range LinearMap.span_singleton_eq_rangeₓ'. -/
+#print LinearMap.span_singleton_eq_range /-
 /-- The range of `to_span_singleton x` is the span of `x`.-/
 theorem span_singleton_eq_range (x : M) : (R ∙ x) = (toSpanSingleton R M x).range :=
   Submodule.ext fun y => by
     refine' Iff.trans _ linear_map.mem_range.symm
     exact mem_span_singleton
 #align linear_map.span_singleton_eq_range LinearMap.span_singleton_eq_range
+-/
 
 /- warning: linear_map.to_span_singleton_one -> LinearMap.toSpanSingleton_one 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (x : M), Eq.{succ u2} M (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3) (fun (_x : LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3) => R -> M) (LinearMap.hasCoeToFun.{u1, u1, u1, u2} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.toSpanSingleton.{u1, u2} R M _inst_1 _inst_2 _inst_3 x) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) x
 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => M) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u2} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.toSpanSingleton.{u1, u2} R M _inst_1 _inst_2 _inst_3 x) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) x
 Case conversion may be inaccurate. Consider using '#align linear_map.to_span_singleton_one LinearMap.toSpanSingleton_oneₓ'. -/
 @[simp]
 theorem toSpanSingleton_one (x : M) : toSpanSingleton R M x 1 = x :=
@@ -1606,7 +1602,7 @@ variable {σ₁₂ : R →+* R₂}
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u3} M} {f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (forall {{x : M}}, (Membership.Mem.{u3, u3} M (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g x)))
 but is expected to have type
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+  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (forall {{x : M}}, (Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u3, u4} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g x)))
 Case conversion may be inaccurate. Consider using '#align linear_map.eq_on_span LinearMap.eqOn_spanₓ'. -/
 /-- If two linear maps are equal on a set `s`, then they are equal on `submodule.span s`.
 
@@ -1619,7 +1615,7 @@ theorem eqOn_span {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (H : Set.EqOn f
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u3} M} {f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Set.EqOn.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)))
 but is expected to have type
-  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) (SetLike.coe.{u4, u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s)))
+  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) (SetLike.coe.{u4, u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s)))
 Case conversion may be inaccurate. Consider using '#align linear_map.eq_on_span' LinearMap.eqOn_span'ₓ'. -/
 /-- If two linear maps are equal on a set `s`, then they are equal on `submodule.span s`.
 
@@ -1634,7 +1630,7 @@ theorem eqOn_span' {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (H : Set.EqOn
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u3} M} {f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Eq.{succ u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s) (Top.top.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.hasTop.{u1, u3} R M _inst_1 _inst_2 _inst_3))) -> (Set.EqOn.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Eq.{max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) f g)
 but is expected to have type
-  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Eq.{succ u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s) (Top.top.{u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.instTopSubmodule.{u3, u4} R M _inst_1 _inst_2 _inst_3))) -> (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Eq.{max (succ u4) (succ u1)} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) f g)
+  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Eq.{succ u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s) (Top.top.{u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.instTopSubmodule.{u3, u4} R M _inst_1 _inst_2 _inst_3))) -> (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Eq.{max (succ u4) (succ u1)} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) f g)
 Case conversion may be inaccurate. Consider using '#align linear_map.ext_on LinearMap.ext_onₓ'. -/
 /-- If `s` generates the whole module and linear maps `f`, `g` are equal on `s`, then they are
 equal. -/
@@ -1646,7 +1642,7 @@ theorem ext_on {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (hv : span R s = 
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {ι : Type.{u5}} {v : ι -> M} {f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Eq.{succ u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 (Set.range.{u3, succ u5} M ι v)) (Top.top.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.hasTop.{u1, u3} R M _inst_1 _inst_2 _inst_3))) -> (forall (i : ι), Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (v i)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g (v i))) -> (Eq.{max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) f g)
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} {ι : Type.{u5}} {v : ι -> M} {f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Eq.{succ u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.range.{u2, succ u5} M ι v)) (Top.top.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.instTopSubmodule.{u4, u2} R M _inst_1 _inst_2 _inst_3))) -> (forall (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) (v i)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (v i)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g (v i))) -> (Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) f g)
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} {ι : Type.{u5}} {v : ι -> M} {f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Eq.{succ u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.range.{u2, succ u5} M ι v)) (Top.top.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.instTopSubmodule.{u4, u2} R M _inst_1 _inst_2 _inst_3))) -> (forall (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) (v i)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (v i)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g (v i))) -> (Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) f g)
 Case conversion may be inaccurate. Consider using '#align linear_map.ext_on_range LinearMap.ext_on_rangeₓ'. -/
 /-- If the range of `v : ι → M` generates the whole module and linear maps `f`, `g` are equal at
 each `v i`, then they are equal. -/
@@ -1669,7 +1665,7 @@ open Classical
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (f : LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) {x : V}, (Ne.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) => V -> K) (LinearMap.hasCoeToFun.{u1, u1, u2, u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f x) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)) (LinearMap.ker.{u1, u1, u2, u1, max u2 u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.semilinearMapClass.{u1, u1, u2, u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f)) (Top.top.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))
 but is expected to have type
-  forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] (f : LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) {x : V}, (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (CommGroupWithZero.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (Semifield.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) _inst_1))))))) -> (Eq.{succ u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Sup.sup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Submodule.span.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3 (Singleton.singleton.{u1, u1} V (Set.{u1} V) (Set.instSingletonSet.{u1} V) x)) (LinearMap.ker.{u2, u2, u1, u2, max u2 u1} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f)) (Top.top.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3)))
+  forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] (f : LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) {x : V}, (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => K) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => K) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => K) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => K) x) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => K) x) (CommGroupWithZero.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => K) x) (Semifield.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => K) x) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => K) x) _inst_1))))))) -> (Eq.{succ u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Sup.sup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Submodule.span.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3 (Singleton.singleton.{u1, u1} V (Set.{u1} V) (Set.instSingletonSet.{u1} V) x)) (LinearMap.ker.{u2, u2, u1, u2, max u2 u1} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (LinearMap.semilinearMapClass.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f)) (Top.top.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3)))
 Case conversion may be inaccurate. Consider using '#align linear_map.span_singleton_sup_ker_eq_top LinearMap.span_singleton_sup_ker_eq_topₓ'. -/
 theorem span_singleton_sup_ker_eq_top (f : V →ₗ[K] K) {x : V} (hx : f x ≠ 0) :
     (K ∙ x) ⊔ f.ker = ⊤ :=
@@ -1688,7 +1684,7 @@ variable (K V)
 lean 3 declaration is
   forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {x : V}, (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (Eq.{succ u1} (Submodule.{u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.ker.{u1, u1, u1, u2, max u1 u2} K K K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, u1, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) K V (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u1, u2} K K K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (LinearMap.toSpanSingleton.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x)) (Bot.bot.{u1} (Submodule.{u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (Submodule.hasBot.{u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {x : V}, (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (Eq.{succ u1} (Submodule.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.ker.{u1, u1, u1, u2, max u1 u2} K K K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) K V (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u2} K K K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.toSpanSingleton.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x)) (Bot.bot.{u1} (Submodule.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Submodule.instBotSubmodule.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))
+  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] {x : V}, (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (Eq.{succ u1} (Submodule.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.ker.{u1, u1, u1, u2, max u1 u2} K K K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (LinearMap.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) K V (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u1, u2} K K K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (LinearMap.toSpanSingleton.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x)) (Bot.bot.{u1} (Submodule.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Submodule.instBotSubmodule.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align linear_map.ker_to_span_singleton LinearMap.ker_toSpanSingletonₓ'. -/
 theorem ker_toSpanSingleton {x : V} (h : x ≠ 0) : (toSpanSingleton K V x).ker = ⊥ :=
   by

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

@@ -75,7 +75,7 @@ theorem subset_span : s ⊆ span R s := fun x h => mem_span.2 fun p hp => hp h
 
 /- warning: submodule.span_le -> Submodule.span_le 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M} {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3}, Iff (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) p) (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 _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M} {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3}, Iff (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) p) (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 _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p))
 but is expected to have type
   forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u1} M} {p : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3}, Iff (LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 s) p) (HasSubset.Subset.{u1} (Set.{u1} M) (Set.instHasSubsetSet.{u1} M) s (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) p))
 Case conversion may be inaccurate. Consider using '#align submodule.span_le Submodule.span_leₓ'. -/
@@ -85,7 +85,7 @@ theorem span_le {p} : span R s ≤ p ↔ s ⊆ p :=
 
 /- warning: submodule.span_mono -> Submodule.span_mono 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M} {t : Set.{u2} M}, (HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) s t) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 t))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M} {t : Set.{u2} M}, (HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) s t) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 t))
 but is expected to have type
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M} {t : Set.{u2} M}, (HasSubset.Subset.{u2} (Set.{u2} M) (Set.instHasSubsetSet.{u2} M) s t) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 t))
 Case conversion may be inaccurate. Consider using '#align submodule.span_mono Submodule.span_monoₓ'. -/
@@ -104,7 +104,7 @@ theorem span_monotone : Monotone (span R : Set M → Submodule R M) := fun _ _ =
 
 /- warning: submodule.span_eq_of_le -> Submodule.span_eq_of_le 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, (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 _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p)) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) p)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, (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 _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p)) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) p)
 but is expected to have type
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, (HasSubset.Subset.{u2} (Set.{u2} M) (Set.instHasSubsetSet.{u2} M) s (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) p)) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) p)
 Case conversion may be inaccurate. Consider using '#align submodule.span_eq_of_le Submodule.span_eq_of_leₓ'. -/
@@ -161,7 +161,7 @@ alias Submodule.map_span ← _root_.linear_map.map_span
 
 /- warning: submodule.map_span_le -> Submodule.map_span_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u3} M) (N : Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)))) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) m s) -> (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
+  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u3} M) (N : Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toHasLe.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)))) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) m s) -> (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 but is expected to have type
   forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M) (N : Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) m s) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) m) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 Case conversion may be inaccurate. Consider using '#align submodule.map_span_le Submodule.map_span_leₓ'. -/
@@ -174,7 +174,7 @@ theorem map_span_le [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂
 
 /- warning: linear_map.map_span_le -> LinearMap.map_span_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u3} M) (N : Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)))) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) m s) -> (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
+  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u3} M) (N : Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toHasLe.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)))) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) m s) -> (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 but is expected to have type
   forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M) (N : Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) m s) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) m) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 Case conversion may be inaccurate. Consider using '#align linear_map.map_span_le LinearMap.map_span_leₓ'. -/
@@ -197,7 +197,7 @@ theorem span_insert_zero : span R (insert (0 : M) s) = span R s :=
 
 /- warning: submodule.span_preimage_le -> Submodule.span_preimage_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u4} M₂), LE.le.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
+  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u4} M₂), LE.le.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
 but is expected to have type
   forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u1} M₂), LE.le.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u4, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
 Case conversion may be inaccurate. Consider using '#align submodule.span_preimage_le Submodule.span_preimage_leₓ'. -/
@@ -211,7 +211,7 @@ theorem span_preimage_le (f : M →ₛₗ[σ₁₂] M₂) (s : Set M₂) :
 
 /- warning: linear_map.span_preimage_le -> LinearMap.span_preimage_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u4} M₂), LE.le.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
+  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u4} M₂), LE.le.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
 but is expected to have type
   forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u1} M₂), LE.le.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u4, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
 Case conversion may be inaccurate. Consider using '#align linear_map.span_preimage_le LinearMap.span_preimage_leₓ'. -/
@@ -230,7 +230,7 @@ theorem closure_subset_span {s : Set M} : (AddSubmonoid.closure s : Set M) ⊆ s
 
 /- warning: submodule.closure_le_to_add_submonoid_span -> Submodule.closure_le_toAddSubmonoid_span 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, LE.le.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Preorder.toLE.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (PartialOrder.toPreorder.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SetLike.partialOrder.{u2, u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) M (AddSubmonoid.setLike.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))) (AddSubmonoid.closure.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) s) (Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, LE.le.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Preorder.toHasLe.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (PartialOrder.toPreorder.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SetLike.partialOrder.{u2, u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) M (AddSubmonoid.setLike.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))) (AddSubmonoid.closure.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) s) (Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, LE.le.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Preorder.toLE.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (PartialOrder.toPreorder.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))))) (AddSubmonoid.closure.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) s) (Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))
 Case conversion may be inaccurate. Consider using '#align submodule.closure_le_to_add_submonoid_span Submodule.closure_le_toAddSubmonoid_spanₓ'. -/
@@ -484,7 +484,7 @@ theorem span_range_eq_iSup {ι : Type _} {v : ι → M} : span R (range v) = ⨆
 
 /- warning: submodule.span_smul_le -> Submodule.span_smul_le 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (s : Set.{u2} M) (r : R), LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (SMul.smul.{u1, u2} R (Set.{u2} M) (Set.smulSet.{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_3))))) r s)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (s : Set.{u2} M) (r : R), LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (SMul.smul.{u1, u2} R (Set.{u2} M) (Set.smulSet.{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_3))))) r s)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (s : Set.{u2} M) (r : R), LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (HSMul.hSMul.{u1, u2, u2} R (Set.{u2} M) (Set.{u2} M) (instHSMul.{u1, u2} R (Set.{u2} M) (Set.smulSet.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3)))))) r s)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)
 Case conversion may be inaccurate. Consider using '#align submodule.span_smul_le Submodule.span_smul_leₓ'. -/
@@ -518,7 +518,7 @@ theorem span_smul_eq_of_isUnit (s : Set M) (r : R) (hr : IsUnit r) : span R (r 
 
 /- warning: submodule.coe_supr_of_directed -> Submodule.coe_iSup_of_directed 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} [hι : Nonempty.{u3} ι] (S : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Directed.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) S) -> (Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u2, u3} M ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (S i))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} [hι : Nonempty.{u3} ι] (S : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Directed.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) S) -> (Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u2, u3} M ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (S i))))
 but is expected to have type
   forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} [hι : Nonempty.{u3} ι] (S : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), (Directed.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.5760 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.5762 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.5760 x._@.Mathlib.LinearAlgebra.Span._hyg.5762) S) -> (Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (iSup.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u1, u3} M ι (fun (i : ι) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (S i))))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_supr_of_directed Submodule.coe_iSup_of_directedₓ'. -/
@@ -539,7 +539,7 @@ theorem coe_iSup_of_directed {ι} [hι : Nonempty ι] (S : ι → Submodule R M)
 
 /- warning: submodule.mem_supr_of_directed -> Submodule.mem_iSup_of_directed 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} [_inst_7 : Nonempty.{u3} ι] (S : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Directed.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) S) -> (forall {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι S)) (Exists.{u3} ι (fun (i : ι) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (S i))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} [_inst_7 : Nonempty.{u3} ι] (S : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Directed.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) S) -> (forall {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι S)) (Exists.{u3} ι (fun (i : ι) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (S i))))
 but is expected to have type
   forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} [_inst_7 : Nonempty.{u3} ι] (S : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), (Directed.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.6058 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.6060 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.6058 x._@.Mathlib.LinearAlgebra.Span._hyg.6060) S) -> (forall {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (iSup.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι S)) (Exists.{u3} ι (fun (i : ι) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (S i))))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_of_directed Submodule.mem_iSup_of_directedₓ'. -/
@@ -553,7 +553,7 @@ theorem mem_iSup_of_directed {ι} [Nonempty ι] (S : ι → Submodule R M) (H :
 
 /- warning: submodule.mem_Sup_of_directed -> Submodule.mem_sSup_of_directed 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {z : M}, (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) s) -> (DirectedOn.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) s) -> (Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (SupSet.sSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) s)) (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (y : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Exists.{0} (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) (fun (H : Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z y))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {z : M}, (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) s) -> (DirectedOn.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) s) -> (Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (SupSet.sSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) s)) (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (y : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Exists.{0} (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) (fun (H : Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z y))))
 but is expected to have type
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {z : M}, (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) s) -> (DirectedOn.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.6191 : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.6193 : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.6191 x._@.Mathlib.LinearAlgebra.Span._hyg.6193) s) -> (Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (SupSet.sSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) s)) (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (y : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => And (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z y))))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_Sup_of_directed Submodule.mem_sSup_of_directedₓ'. -/
@@ -716,7 +716,7 @@ theorem mem_span_singleton {y : M} : (x ∈ R ∙ y) ↔ ∃ a : R, a • y = x
 
 /- warning: submodule.le_span_singleton_iff -> Submodule.le_span_singleton_iff 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {v₀ : M}, Iff (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) s (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) v₀))) (forall (v : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) v s) -> (Exists.{succ u1} R (fun (r : R) => Eq.{succ u2} M (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_3)))) r v₀) v)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {v₀ : M}, Iff (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) s (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) v₀))) (forall (v : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) v s) -> (Exists.{succ u1} R (fun (r : R) => Eq.{succ u2} M (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_3)))) r v₀) v)))
 but is expected to have type
   forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3} {v₀ : M}, Iff (LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) s (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) v₀))) (forall (v : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) v s) -> (Exists.{succ u2} R (fun (r : R) => Eq.{succ u1} M (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_3))))) r v₀) v)))
 Case conversion may be inaccurate. Consider using '#align submodule.le_span_singleton_iff Submodule.le_span_singleton_iffₓ'. -/
@@ -759,7 +759,7 @@ theorem span_singleton_eq_range (y : M) : ↑(R ∙ y) = range ((· • y) : R 
 
 /- warning: submodule.span_singleton_smul_le -> Submodule.span_singleton_smul_le 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {S : Type.{u3}} [_inst_7 : Monoid.{u3} S] [_inst_8 : SMul.{u3, u1} S R] [_inst_9 : MulAction.{u3, u2} S M _inst_7] [_inst_10 : IsScalarTower.{u3, u1, u2} S R M _inst_8 (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_3)))) (MulAction.toHasSmul.{u3, u2} S M _inst_7 _inst_9)] (r : S) (x : M), LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) (SMul.smul.{u3, u2} S M (MulAction.toHasSmul.{u3, u2} S M _inst_7 _inst_9) r x))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))
+  forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {S : Type.{u3}} [_inst_7 : Monoid.{u3} S] [_inst_8 : SMul.{u3, u1} S R] [_inst_9 : MulAction.{u3, u2} S M _inst_7] [_inst_10 : IsScalarTower.{u3, u1, u2} S R M _inst_8 (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_3)))) (MulAction.toHasSmul.{u3, u2} S M _inst_7 _inst_9)] (r : S) (x : M), LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) (SMul.smul.{u3, u2} S M (MulAction.toHasSmul.{u3, u2} S M _inst_7 _inst_9) r x))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))
 but is expected to have type
   forall (R : Type.{u2}) {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {S : Type.{u3}} [_inst_7 : Monoid.{u3} S] [_inst_8 : SMul.{u3, u2} S R] [_inst_9 : MulAction.{u3, u1} S M _inst_7] [_inst_10 : IsScalarTower.{u3, u2, u1} S R M _inst_8 (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_3)))) (MulAction.toSMul.{u3, u1} S M _inst_7 _inst_9)] (r : S) (x : M), LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) (HSMul.hSMul.{u3, u1, u1} S M M (instHSMul.{u3, u1} S M (MulAction.toSMul.{u3, u1} S M _inst_7 _inst_9)) r x))) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) x))
 Case conversion may be inaccurate. Consider using '#align submodule.span_singleton_smul_le Submodule.span_singleton_smul_leₓ'. -/
@@ -886,7 +886,7 @@ variable (R S s)
 
 /- warning: submodule.span_le_restrict_scalars -> Submodule.span_le_restrictScalars is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) {M : Type.{u2}} (S : Type.{u3}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (s : Set.{u2} M) [_inst_7 : Semiring.{u3} S] [_inst_8 : SMul.{u1, u3} R S] [_inst_9 : Module.{u3, u2} S M _inst_7 _inst_2] [_inst_10 : IsScalarTower.{u1, u3, u2} R S M _inst_8 (SMulZeroClass.toHasSmul.{u3, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u3, u2} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_7)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u3, u2} S M (Semiring.toMonoidWithZero.{u3} S _inst_7) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u3, u2} S M _inst_7 _inst_2 _inst_9)))) (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_3))))], LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) (Submodule.restrictScalars.{u1, u3, u2} R S M _inst_7 _inst_2 _inst_1 _inst_3 _inst_9 _inst_8 _inst_10 (Submodule.span.{u3, u2} S M _inst_7 _inst_2 _inst_9 s))
+  forall (R : Type.{u1}) {M : Type.{u2}} (S : Type.{u3}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (s : Set.{u2} M) [_inst_7 : Semiring.{u3} S] [_inst_8 : SMul.{u1, u3} R S] [_inst_9 : Module.{u3, u2} S M _inst_7 _inst_2] [_inst_10 : IsScalarTower.{u1, u3, u2} R S M _inst_8 (SMulZeroClass.toHasSmul.{u3, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u3, u2} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_7)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u3, u2} S M (Semiring.toMonoidWithZero.{u3} S _inst_7) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u3, u2} S M _inst_7 _inst_2 _inst_9)))) (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_3))))], LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) (Submodule.restrictScalars.{u1, u3, u2} R S M _inst_7 _inst_2 _inst_1 _inst_3 _inst_9 _inst_8 _inst_10 (Submodule.span.{u3, u2} S M _inst_7 _inst_2 _inst_9 s))
 but is expected to have type
   forall (R : Type.{u2}) {M : Type.{u1}} (S : Type.{u3}) [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] (s : Set.{u1} M) [_inst_7 : Semiring.{u3} S] [_inst_8 : SMul.{u2, u3} R S] [_inst_9 : Module.{u3, u1} S M _inst_7 _inst_2] [_inst_10 : IsScalarTower.{u2, u3, u1} R S M _inst_8 (SMulZeroClass.toSMul.{u3, u1} S M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u1} S M (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_7)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S _inst_7) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u3, u1} S M _inst_7 _inst_2 _inst_9)))) (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_3))))], LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 s) (Submodule.restrictScalars.{u2, u3, u1} R S M _inst_7 _inst_2 _inst_1 _inst_3 _inst_9 _inst_8 _inst_10 (Submodule.span.{u3, u1} S M _inst_7 _inst_2 _inst_9 s))
 Case conversion may be inaccurate. Consider using '#align submodule.span_le_restrict_scalars Submodule.span_le_restrictScalarsₓ'. -/
@@ -1134,7 +1134,7 @@ theorem iSup_induction' {ι : Sort _} (p : ι → Submodule R M) {C : ∀ x, (x
 
 /- warning: submodule.span_singleton_le_iff_mem -> Submodule.span_singleton_le_iff_mem 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (m : M) (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), Iff (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) m)) p) (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m p)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (m : M) (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), Iff (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) m)) p) (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m p)
 but is expected to have type
   forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] (m : M) (p : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), Iff (LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) m)) p) (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m p)
 Case conversion may be inaccurate. Consider using '#align submodule.span_singleton_le_iff_mem Submodule.span_singleton_le_iff_memₓ'. -/
@@ -1208,7 +1208,7 @@ theorem submodule_eq_sSup_le_nonzero_spans (p : Submodule R M) :
 
 /- warning: submodule.lt_sup_iff_not_mem -> Submodule.lt_sup_iff_not_mem 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {a : M}, Iff (LT.lt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) I (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) I (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) a)))) (Not (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) a I))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {a : M}, Iff (LT.lt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) I (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) I (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) a)))) (Not (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) a I))
 but is expected to have type
   forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {I : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3} {a : M}, Iff (LT.lt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) I (Sup.sup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) I (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) a)))) (Not (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) a I))
 Case conversion may be inaccurate. Consider using '#align submodule.lt_sup_iff_not_mem Submodule.lt_sup_iff_not_memₓ'. -/
@@ -1238,7 +1238,7 @@ theorem lt_sup_iff_not_mem {I : Submodule R M} {a : M} : (I < I ⊔ R ∙ a) ↔
 
 /- warning: submodule.mem_supr -> Submodule.mem_iSup 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) {m : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (forall (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (forall (i : ι), LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (p i) N) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m N))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) {m : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (forall (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (forall (i : ι), LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (p i) N) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m N))
 but is expected to have type
   forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) {m : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (iSup.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (forall (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), (forall (i : ι), LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (p i) N) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m N))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr Submodule.mem_iSupₓ'. -/
@@ -1322,7 +1322,7 @@ theorem mem_prod {p : Submodule R M} {q : Submodule R M'} {x : M × M'} :
 
 /- warning: submodule.span_prod_le -> Submodule.span_prod_le 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {M' : Type.{u3}} [_inst_7 : AddCommMonoid.{u3} M'] [_inst_8 : Module.{u1, u3} R M' _inst_1 _inst_7] (s : Set.{u2} M) (t : Set.{u3} M'), LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Prod.{u2, u3} M M') (Submodule.setLike.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8))))) (Submodule.span.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8) (Set.prod.{u2, u3} M M' s t)) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) M' _inst_7 _inst_8 (Submodule.span.{u1, u3} R M' _inst_1 _inst_7 _inst_8 t))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {M' : Type.{u3}} [_inst_7 : AddCommMonoid.{u3} M'] [_inst_8 : Module.{u1, u3} R M' _inst_1 _inst_7] (s : Set.{u2} M) (t : Set.{u3} M'), LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Preorder.toHasLe.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Prod.{u2, u3} M M') (Submodule.setLike.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8))))) (Submodule.span.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8) (Set.prod.{u2, u3} M M' s t)) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) M' _inst_7 _inst_8 (Submodule.span.{u1, u3} R M' _inst_1 _inst_7 _inst_8 t))
 but is expected to have type
   forall {R : Type.{u1}} {M : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] {M' : Type.{u2}} [_inst_7 : AddCommMonoid.{u2} M'] [_inst_8 : Module.{u1, u2} R M' _inst_1 _inst_7] (s : Set.{u3} M) (t : Set.{u2} M'), LE.le.{max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Submodule.completeLattice.{u1, max u3 u2} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)))))) (Submodule.span.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8) (Set.prod.{u3, u2} M M' s t)) (Submodule.prod.{u1, u3, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s) M' _inst_7 _inst_8 (Submodule.span.{u1, u2} R M' _inst_1 _inst_7 _inst_8 t))
 Case conversion may be inaccurate. Consider using '#align submodule.span_prod_le Submodule.span_prod_leₓ'. -/
@@ -1353,7 +1353,7 @@ theorem prod_bot : (prod ⊥ ⊥ : Submodule R (M × M')) = ⊥ := by ext ⟨x,
 
 /- warning: submodule.prod_mono -> Submodule.prod_mono 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {M' : Type.{u3}} [_inst_7 : AddCommMonoid.{u3} M'] [_inst_8 : Module.{u1, u3} R M' _inst_1 _inst_7] {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {q : Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8} {q' : Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8}, (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p p') -> (LE.le.{u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (Preorder.toLE.{u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) M' (Submodule.setLike.{u1, u3} R M' _inst_1 _inst_7 _inst_8)))) q q') -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Prod.{u2, u3} M M') (Submodule.setLike.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8))))) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 p M' _inst_7 _inst_8 q) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 p' M' _inst_7 _inst_8 q'))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {M' : Type.{u3}} [_inst_7 : AddCommMonoid.{u3} M'] [_inst_8 : Module.{u1, u3} R M' _inst_1 _inst_7] {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {q : Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8} {q' : Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8}, (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p p') -> (LE.le.{u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (Preorder.toHasLe.{u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) M' (Submodule.setLike.{u1, u3} R M' _inst_1 _inst_7 _inst_8)))) q q') -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Preorder.toHasLe.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (SetLike.partialOrder.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Prod.{u2, u3} M M') (Submodule.setLike.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8))))) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 p M' _inst_7 _inst_8 q) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 p' M' _inst_7 _inst_8 q'))
 but is expected to have type
   forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {M' : Type.{u1}} [_inst_7 : AddCommMonoid.{u1} M'] [_inst_8 : Module.{u3, u1} R M' _inst_1 _inst_7] {p : Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_3} {p' : Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_3} {q : Submodule.{u3, u1} R M' _inst_1 _inst_7 _inst_8} {q' : Submodule.{u3, u1} R M' _inst_1 _inst_7 _inst_8}, (LE.le.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u3, u2} R M _inst_1 _inst_2 _inst_3))))) p p') -> (LE.le.{u1} (Submodule.{u3, u1} R M' _inst_1 _inst_7 _inst_8) (Preorder.toLE.{u1} (Submodule.{u3, u1} R M' _inst_1 _inst_7 _inst_8) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R M' _inst_1 _inst_7 _inst_8) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R M' _inst_1 _inst_7 _inst_8) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R M' _inst_1 _inst_7 _inst_8) (Submodule.completeLattice.{u3, u1} R M' _inst_1 _inst_7 _inst_8))))) q q') -> (LE.le.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u1} M M' _inst_2 _inst_7) (Prod.module.{u3, u2, u1} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Preorder.toLE.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u1} M M' _inst_2 _inst_7) (Prod.module.{u3, u2, u1} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (PartialOrder.toPreorder.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u1} M M' _inst_2 _inst_7) (Prod.module.{u3, u2, u1} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u1} M M' _inst_2 _inst_7) (Prod.module.{u3, u2, u1} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u1} M M' _inst_2 _inst_7) (Prod.module.{u3, u2, u1} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Submodule.completeLattice.{u3, max u2 u1} R (Prod.{u2, u1} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u1} M M' _inst_2 _inst_7) (Prod.module.{u3, u2, u1} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)))))) (Submodule.prod.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 p M' _inst_7 _inst_8 q) (Submodule.prod.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 p' M' _inst_7 _inst_8 q'))
 Case conversion may be inaccurate. Consider using '#align submodule.prod_mono Submodule.prod_monoₓ'. -/
@@ -1465,7 +1465,7 @@ theorem comap_map_eq (f : F) (p : Submodule R M) : comap f (map f p) = p ⊔ Lin
 
 /- warning: submodule.comap_map_eq_self -> Submodule.comap_map_eq_self is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u5}} [sc : SemilinearMapClass.{u5, u1, u2, u3, u4} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_4 _inst_6] {f : F} {p : Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4}, (LE.le.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (Preorder.toLE.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4)))) (LinearMap.ker.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ F sc f) p) -> (Eq.{succ u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (Submodule.comap.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ F sc f (Submodule.map.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ _inst_7 F sc f p)) p)
+  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u5}} [sc : SemilinearMapClass.{u5, u1, u2, u3, u4} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_4 _inst_6] {f : F} {p : Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4}, (LE.le.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (Preorder.toHasLe.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4)))) (LinearMap.ker.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ F sc f) p) -> (Eq.{succ u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (Submodule.comap.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ F sc f (Submodule.map.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ _inst_7 F sc f p)) p)
 but is expected to have type
   forall {R : Type.{u5}} {R₂ : Type.{u3}} {M : Type.{u4}} {M₂ : Type.{u2}} [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u3} R₂] [_inst_3 : AddCommGroup.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3)] [_inst_5 : AddCommGroup.{u2} M₂] [_inst_6 : Module.{u3, u2} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_5)] {τ₁₂ : RingHom.{u5, u3} R R₂ (Semiring.toNonAssocSemiring.{u5} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u5, u3} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u1}} [sc : SemilinearMapClass.{u1, u5, u3, u4, u2} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_5) _inst_4 _inst_6] {f : F} {p : Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4}, (LE.le.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) (Preorder.toLE.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) (Submodule.completeLattice.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4))))) (LinearMap.ker.{u5, u3, u4, u2, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ F sc f) p) -> (Eq.{succ u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) (Submodule.comap.{u5, u3, u4, u2, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ F sc f (Submodule.map.{u5, u3, u4, u2, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ _inst_7 F sc f p)) p)
 Case conversion may be inaccurate. Consider using '#align submodule.comap_map_eq_self Submodule.comap_map_eq_selfₓ'. -/
@@ -1501,7 +1501,7 @@ include sc
 
 /- warning: linear_map.map_le_map_iff -> LinearMap.map_le_map_iff is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : AddCommGroup.{u4} M₂] [_inst_5 : Module.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4)] {τ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u5}} [sc : SemilinearMapClass.{u5, u1, u2, u3, u4} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6] (f : F) {p : Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5} {p' : Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5}, Iff (LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (Preorder.toLE.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6)))) (Submodule.map.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p) (Submodule.map.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p')) (LE.le.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Preorder.toLE.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) M (Submodule.setLike.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5)))) p (Sup.sup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (SemilatticeSup.toHasSup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Lattice.toSemilatticeSup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (ConditionallyCompleteLattice.toLattice.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Submodule.completeLattice.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5))))) p' (LinearMap.ker.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ F sc f)))
+  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : AddCommGroup.{u4} M₂] [_inst_5 : Module.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4)] {τ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u5}} [sc : SemilinearMapClass.{u5, u1, u2, u3, u4} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6] (f : F) {p : Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5} {p' : Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5}, Iff (LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (Preorder.toHasLe.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6)))) (Submodule.map.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p) (Submodule.map.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p')) (LE.le.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Preorder.toHasLe.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) M (Submodule.setLike.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5)))) p (Sup.sup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (SemilatticeSup.toHasSup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Lattice.toSemilatticeSup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (ConditionallyCompleteLattice.toLattice.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Submodule.completeLattice.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5))))) p' (LinearMap.ker.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ F sc f)))
 but is expected to have type
   forall {R : Type.{u5}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u3}} [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : AddCommGroup.{u4} M] [_inst_4 : AddCommGroup.{u3} M₂] [_inst_5 : Module.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3)] [_inst_6 : Module.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4)] {τ₁₂ : RingHom.{u5, u2} R R₂ (Semiring.toNonAssocSemiring.{u5} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u5, u2} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u1}} [sc : SemilinearMapClass.{u1, u5, u2, u4, u3} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5 _inst_6] (f : F) {p : Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5} {p' : Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5}, Iff (LE.le.{u3} (Submodule.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_6) (Preorder.toLE.{u3} (Submodule.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_6) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_6) (Submodule.completeLattice.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_6))))) (Submodule.map.{u5, u2, u4, u3, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p) (Submodule.map.{u5, u2, u4, u3, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p')) (LE.le.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (Preorder.toLE.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (PartialOrder.toPreorder.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (Submodule.completeLattice.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5))))) p (Sup.sup.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (SemilatticeSup.toSup.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (Lattice.toSemilatticeSup.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (ConditionallyCompleteLattice.toLattice.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (Submodule.completeLattice.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5))))) p' (LinearMap.ker.{u5, u2, u4, u3, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ F sc f)))
 Case conversion may be inaccurate. Consider using '#align linear_map.map_le_map_iff LinearMap.map_le_map_iffₓ'. -/
@@ -1511,7 +1511,7 @@ protected theorem map_le_map_iff (f : F) {p p'} : map f p ≤ map f p' ↔ p ≤
 
 /- warning: linear_map.map_le_map_iff' -> LinearMap.map_le_map_iff' is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : AddCommGroup.{u4} M₂] [_inst_5 : Module.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4)] {τ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u5}} [sc : SemilinearMapClass.{u5, u1, u2, u3, u4} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6] {f : F}, (Eq.{succ u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (LinearMap.ker.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ F sc f) (Bot.bot.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Submodule.hasBot.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5))) -> (forall {p : Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5} {p' : Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5}, Iff (LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (Preorder.toLE.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6)))) (Submodule.map.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p) (Submodule.map.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p')) (LE.le.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Preorder.toLE.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) M (Submodule.setLike.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5)))) p p'))
+  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : AddCommGroup.{u4} M₂] [_inst_5 : Module.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4)] {τ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u5}} [sc : SemilinearMapClass.{u5, u1, u2, u3, u4} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6] {f : F}, (Eq.{succ u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (LinearMap.ker.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ F sc f) (Bot.bot.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Submodule.hasBot.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5))) -> (forall {p : Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5} {p' : Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5}, Iff (LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (Preorder.toHasLe.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6)))) (Submodule.map.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p) (Submodule.map.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p')) (LE.le.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Preorder.toHasLe.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) M (Submodule.setLike.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5)))) p p'))
 but is expected to have type
   forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u5}} {M₂ : Type.{u2}} [_inst_1 : Semiring.{u4} R] [_inst_2 : Semiring.{u3} R₂] [_inst_3 : AddCommGroup.{u5} M] [_inst_4 : AddCommGroup.{u2} M₂] [_inst_5 : Module.{u4, u5} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u5} M _inst_3)] [_inst_6 : Module.{u3, u2} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_4)] {τ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u1}} [sc : SemilinearMapClass.{u1, u4, u3, u5, u2} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u5} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_4) _inst_5 _inst_6] {f : F}, (Eq.{succ u5} (Submodule.{u4, u5} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u5} M _inst_3) _inst_5) (LinearMap.ker.{u4, u3, u5, u2, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u5} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ F sc f) (Bot.bot.{u5} (Submodule.{u4, u5} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u5} M _inst_3) _inst_5) (Submodule.instBotSubmodule.{u4, u5} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u5} M _inst_3) _inst_5))) -> (forall {p : Submodule.{u4, u5} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u5} M _inst_3) _inst_5} {p' : Submodule.{u4, u5} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u5} M _inst_3) _inst_5}, Iff (LE.le.{u2} (Submodule.{u3, u2} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_4) _inst_6) (Preorder.toLE.{u2} (Submodule.{u3, u2} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_4) _inst_6) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_4) _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_4) _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_4) _inst_6) (Submodule.completeLattice.{u3, u2} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_4) _inst_6))))) (Submodule.map.{u4, u3, u5, u2, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u5} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p) (Submodule.map.{u4, u3, u5, u2, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u5} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p')) (LE.le.{u5} (Submodule.{u4, u5} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u5} M _inst_3) _inst_5) (Preorder.toLE.{u5} (Submodule.{u4, u5} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u5} M _inst_3) _inst_5) (PartialOrder.toPreorder.{u5} (Submodule.{u4, u5} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u5} M _inst_3) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u5} (Submodule.{u4, u5} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u5} M _inst_3) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u5} (Submodule.{u4, u5} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u5} M _inst_3) _inst_5) (Submodule.completeLattice.{u4, u5} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u5} M _inst_3) _inst_5))))) p p'))
 Case conversion may be inaccurate. Consider using '#align linear_map.map_le_map_iff' LinearMap.map_le_map_iff'ₓ'. -/

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

@@ -54,7 +54,7 @@ variable (R)
 #print Submodule.span /-
 /-- The span of a set `s ⊆ M` is the smallest submodule of M that contains `s`. -/
 def span (s : Set M) : Submodule R M :=
-  infₛ { p | s ⊆ p }
+  sInf { p | s ⊆ p }
 #align submodule.span Submodule.span
 -/
 
@@ -64,7 +64,7 @@ variable {s t : Set M}
 
 #print Submodule.mem_span /-
 theorem mem_span : x ∈ span R s ↔ ∀ p : Submodule R M, s ⊆ p → x ∈ p :=
-  mem_interᵢ₂
+  mem_iInter₂
 #align submodule.mem_span Submodule.mem_span
 -/
 
@@ -405,38 +405,38 @@ theorem span_union (s t : Set M) : span R (s ∪ t) = span R s ⊔ span R t :=
   (Submodule.gi R M).gc.l_sup
 #align submodule.span_union Submodule.span_union
 
-/- warning: submodule.span_Union -> Submodule.span_unionᵢ is a dubious translation:
+/- warning: submodule.span_Union -> Submodule.span_iUnion 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (s : ι -> (Set.{u2} M)), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.unionᵢ.{u2, u3} M ι (fun (i : ι) => s i))) (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (s i)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (s : ι -> (Set.{u2} M)), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.iUnion.{u2, u3} M ι (fun (i : ι) => s i))) (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (s i)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (s : ι -> (Set.{u2} M)), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.unionᵢ.{u2, u3} M ι (fun (i : ι) => s i))) (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (s i)))
-Case conversion may be inaccurate. Consider using '#align submodule.span_Union Submodule.span_unionᵢₓ'. -/
-theorem span_unionᵢ {ι} (s : ι → Set M) : span R (⋃ i, s i) = ⨆ i, span R (s i) :=
-  (Submodule.gi R M).gc.l_supᵢ
-#align submodule.span_Union Submodule.span_unionᵢ
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (s : ι -> (Set.{u2} M)), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.iUnion.{u2, u3} M ι (fun (i : ι) => s i))) (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (s i)))
+Case conversion may be inaccurate. Consider using '#align submodule.span_Union Submodule.span_iUnionₓ'. -/
+theorem span_iUnion {ι} (s : ι → Set M) : span R (⋃ i, s i) = ⨆ i, span R (s i) :=
+  (Submodule.gi R M).gc.l_iSup
+#align submodule.span_Union Submodule.span_iUnion
 
-/- warning: submodule.span_Union₂ -> Submodule.span_unionᵢ₂ is a dubious translation:
+/- warning: submodule.span_Union₂ -> Submodule.span_iUnion₂ 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} (s : forall (i : ι), (κ i) -> (Set.{u2} M)), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.unionᵢ.{u2, u3} M ι (fun (i : ι) => Set.unionᵢ.{u2, u4} M (κ i) (fun (j : κ i) => s i j)))) (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u2, u4} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (κ i) (fun (j : κ i) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (s i j))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} (s : forall (i : ι), (κ i) -> (Set.{u2} M)), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.iUnion.{u2, u3} M ι (fun (i : ι) => Set.iUnion.{u2, u4} M (κ i) (fun (j : κ i) => s i j)))) (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => iSup.{u2, u4} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (κ i) (fun (j : κ i) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (s i j))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u4}} {κ : ι -> Sort.{u3}} (s : forall (i : ι), (κ i) -> (Set.{u2} M)), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.unionᵢ.{u2, u4} M ι (fun (i : ι) => Set.unionᵢ.{u2, u3} M (κ i) (fun (j : κ i) => s i j)))) (supᵢ.{u2, u4} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (κ i) (fun (j : κ i) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (s i j))))
-Case conversion may be inaccurate. Consider using '#align submodule.span_Union₂ Submodule.span_unionᵢ₂ₓ'. -/
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u4}} {κ : ι -> Sort.{u3}} (s : forall (i : ι), (κ i) -> (Set.{u2} M)), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.iUnion.{u2, u4} M ι (fun (i : ι) => Set.iUnion.{u2, u3} M (κ i) (fun (j : κ i) => s i j)))) (iSup.{u2, u4} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (κ i) (fun (j : κ i) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (s i j))))
+Case conversion may be inaccurate. Consider using '#align submodule.span_Union₂ Submodule.span_iUnion₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem span_unionᵢ₂ {ι} {κ : ι → Sort _} (s : ∀ i, κ i → Set M) :
+theorem span_iUnion₂ {ι} {κ : ι → Sort _} (s : ∀ i, κ i → Set M) :
     span R (⋃ (i) (j), s i j) = ⨆ (i) (j), span R (s i j) :=
-  (Submodule.gi R M).gc.l_supᵢ₂
-#align submodule.span_Union₂ Submodule.span_unionᵢ₂
+  (Submodule.gi R M).gc.l_iSup₂
+#align submodule.span_Union₂ Submodule.span_iUnion₂
 
-/- warning: submodule.span_attach_bUnion -> Submodule.span_attach_bunionᵢ is a dubious translation:
+/- warning: submodule.span_attach_bUnion -> Submodule.span_attach_biUnion 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_7 : DecidableEq.{succ u2} M] {α : Type.{u3}} (s : Finset.{u3} α) (f : (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} α) Type.{u3} (Finset.hasCoeToSort.{u3} α) s) -> (Finset.{u2} M)), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} M) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} M) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} M) (Set.{u2} M) (Finset.Set.hasCoeT.{u2} M))) (Finset.bunionᵢ.{u3, u2} (Subtype.{succ u3} α (fun (x : α) => Membership.Mem.{u3, u3} α (Finset.{u3} α) (Finset.hasMem.{u3} α) x s)) M (fun (a : M) (b : M) => _inst_7 a b) (Finset.attach.{u3} α s) f))) (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} α) Type.{u3} (Finset.hasCoeToSort.{u3} α) s) (fun (x : coeSort.{succ u3, succ (succ u3)} (Finset.{u3} α) Type.{u3} (Finset.hasCoeToSort.{u3} α) s) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} M) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} M) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} M) (Set.{u2} M) (Finset.Set.hasCoeT.{u2} M))) (f x))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_7 : DecidableEq.{succ u2} M] {α : Type.{u3}} (s : Finset.{u3} α) (f : (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} α) Type.{u3} (Finset.hasCoeToSort.{u3} α) s) -> (Finset.{u2} M)), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} M) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} M) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} M) (Set.{u2} M) (Finset.Set.hasCoeT.{u2} M))) (Finset.biUnion.{u3, u2} (Subtype.{succ u3} α (fun (x : α) => Membership.Mem.{u3, u3} α (Finset.{u3} α) (Finset.hasMem.{u3} α) x s)) M (fun (a : M) (b : M) => _inst_7 a b) (Finset.attach.{u3} α s) f))) (iSup.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (coeSort.{succ u3, succ (succ u3)} (Finset.{u3} α) Type.{u3} (Finset.hasCoeToSort.{u3} α) s) (fun (x : coeSort.{succ u3, succ (succ u3)} (Finset.{u3} α) Type.{u3} (Finset.hasCoeToSort.{u3} α) s) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} M) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} M) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} M) (Set.{u2} M) (Finset.Set.hasCoeT.{u2} M))) (f x))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_7 : DecidableEq.{succ u3} M] {α : Type.{u2}} (s : Finset.{u2} α) (f : (Subtype.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Finset.{u2} α) (Finset.instMembershipFinset.{u2} α) x s)) -> (Finset.{u3} M)), Eq.{succ u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 (Finset.toSet.{u3} M (Finset.bunionᵢ.{u2, u3} (Subtype.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Finset.{u2} α) (Finset.instMembershipFinset.{u2} α) x s)) M (fun (a : M) (b : M) => _inst_7 a b) (Finset.attach.{u2} α s) f))) (supᵢ.{u3, succ u2} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u3} R M _inst_1 _inst_2 _inst_3))) (Subtype.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Finset.{u2} α) (Finset.instMembershipFinset.{u2} α) x s)) (fun (x : Subtype.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Finset.{u2} α) (Finset.instMembershipFinset.{u2} α) x s)) => Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 (Finset.toSet.{u3} M (f x))))
-Case conversion may be inaccurate. Consider using '#align submodule.span_attach_bUnion Submodule.span_attach_bunionᵢₓ'. -/
-theorem span_attach_bunionᵢ [DecidableEq M] {α : Type _} (s : Finset α) (f : s → Finset M) :
-    span R (s.attach.bunionᵢ f : Set M) = ⨆ x, span R (f x) := by simpa [span_Union]
-#align submodule.span_attach_bUnion Submodule.span_attach_bunionᵢ
+  forall {R : Type.{u1}} {M : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_7 : DecidableEq.{succ u3} M] {α : Type.{u2}} (s : Finset.{u2} α) (f : (Subtype.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Finset.{u2} α) (Finset.instMembershipFinset.{u2} α) x s)) -> (Finset.{u3} M)), Eq.{succ u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 (Finset.toSet.{u3} M (Finset.biUnion.{u2, u3} (Subtype.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Finset.{u2} α) (Finset.instMembershipFinset.{u2} α) x s)) M (fun (a : M) (b : M) => _inst_7 a b) (Finset.attach.{u2} α s) f))) (iSup.{u3, succ u2} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u3} R M _inst_1 _inst_2 _inst_3))) (Subtype.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Finset.{u2} α) (Finset.instMembershipFinset.{u2} α) x s)) (fun (x : Subtype.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Finset.{u2} α) (Finset.instMembershipFinset.{u2} α) x s)) => Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 (Finset.toSet.{u3} M (f x))))
+Case conversion may be inaccurate. Consider using '#align submodule.span_attach_bUnion Submodule.span_attach_biUnionₓ'. -/
+theorem span_attach_biUnion [DecidableEq M] {α : Type _} (s : Finset α) (f : s → Finset M) :
+    span R (s.attach.biUnion f : Set M) = ⨆ x, span R (f x) := by simpa [span_Union]
+#align submodule.span_attach_bUnion Submodule.span_attach_biUnion
 
 /- warning: submodule.sup_span -> Submodule.sup_span is a dubious translation:
 lean 3 declaration is
@@ -462,25 +462,25 @@ notation:1000
 character `•` U+2022 and the matrix multiplication character `⬝` U+2B1D. -/
 R " ∙ " x => span R (@singleton _ _ Set.hasSingleton x)
 
-/- warning: submodule.span_eq_supr_of_singleton_spans -> Submodule.span_eq_supᵢ_of_singleton_spans is a dubious translation:
+/- warning: submodule.span_eq_supr_of_singleton_spans -> Submodule.span_eq_iSup_of_singleton_spans 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (s : Set.{u2} M), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) (supᵢ.{u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) M (fun (x : M) => supᵢ.{u2, 0} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s) (fun (H : Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (s : Set.{u2} M), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) (iSup.{u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) M (fun (x : M) => iSup.{u2, 0} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s) (fun (H : Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (s : Set.{u2} M), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) (supᵢ.{u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) M (fun (x : M) => supᵢ.{u2, 0} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) (fun (H : Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))))
-Case conversion may be inaccurate. Consider using '#align submodule.span_eq_supr_of_singleton_spans Submodule.span_eq_supᵢ_of_singleton_spansₓ'. -/
-theorem span_eq_supᵢ_of_singleton_spans (s : Set M) : span R s = ⨆ x ∈ s, R ∙ x := by
-  simp only [← span_Union, Set.bunionᵢ_of_singleton s]
-#align submodule.span_eq_supr_of_singleton_spans Submodule.span_eq_supᵢ_of_singleton_spans
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (s : Set.{u2} M), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) (iSup.{u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) M (fun (x : M) => iSup.{u2, 0} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) (fun (H : Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))))
+Case conversion may be inaccurate. Consider using '#align submodule.span_eq_supr_of_singleton_spans Submodule.span_eq_iSup_of_singleton_spansₓ'. -/
+theorem span_eq_iSup_of_singleton_spans (s : Set M) : span R s = ⨆ x ∈ s, R ∙ x := by
+  simp only [← span_Union, Set.biUnion_of_singleton s]
+#align submodule.span_eq_supr_of_singleton_spans Submodule.span_eq_iSup_of_singleton_spans
 
-/- warning: submodule.span_range_eq_supr -> Submodule.span_range_eq_supᵢ is a dubious translation:
+/- warning: submodule.span_range_eq_supr -> Submodule.span_range_eq_iSup 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Type.{u3}} {v : ι -> M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.range.{u2, succ u3} M ι v)) (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) (v i))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Type.{u3}} {v : ι -> M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.range.{u2, succ u3} M ι v)) (iSup.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) (v i))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Type.{u3}} {v : ι -> M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.range.{u2, succ u3} M ι v)) (supᵢ.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) (v i))))
-Case conversion may be inaccurate. Consider using '#align submodule.span_range_eq_supr Submodule.span_range_eq_supᵢₓ'. -/
-theorem span_range_eq_supᵢ {ι : Type _} {v : ι → M} : span R (range v) = ⨆ i, R ∙ v i := by
-  rw [span_eq_supr_of_singleton_spans, supᵢ_range]
-#align submodule.span_range_eq_supr Submodule.span_range_eq_supᵢ
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Type.{u3}} {v : ι -> M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.range.{u2, succ u3} M ι v)) (iSup.{u2, succ u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) (v i))))
+Case conversion may be inaccurate. Consider using '#align submodule.span_range_eq_supr Submodule.span_range_eq_iSupₓ'. -/
+theorem span_range_eq_iSup {ι : Type _} {v : ι → M} : span R (range v) = ⨆ i, R ∙ v i := by
+  rw [span_eq_supr_of_singleton_spans, iSup_range]
+#align submodule.span_range_eq_supr Submodule.span_range_eq_iSup
 
 /- warning: submodule.span_smul_le -> Submodule.span_smul_le is a dubious translation:
 lean 3 declaration is
@@ -516,17 +516,17 @@ theorem span_smul_eq_of_isUnit (s : Set M) (r : R) (hr : IsUnit r) : span R (r 
 #align submodule.span_smul_eq_of_is_unit Submodule.span_smul_eq_of_isUnit
 -/
 
-/- warning: submodule.coe_supr_of_directed -> Submodule.coe_supᵢ_of_directed is a dubious translation:
+/- warning: submodule.coe_supr_of_directed -> Submodule.coe_iSup_of_directed 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} [hι : Nonempty.{u3} ι] (S : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Directed.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) S) -> (Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u2, u3} M ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (S i))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} [hι : Nonempty.{u3} ι] (S : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Directed.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) S) -> (Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u2, u3} M ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (S i))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} [hι : Nonempty.{u3} ι] (S : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), (Directed.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.5760 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.5762 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.5760 x._@.Mathlib.LinearAlgebra.Span._hyg.5762) S) -> (Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u1, u3} M ι (fun (i : ι) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (S i))))
-Case conversion may be inaccurate. Consider using '#align submodule.coe_supr_of_directed Submodule.coe_supᵢ_of_directedₓ'. -/
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} [hι : Nonempty.{u3} ι] (S : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), (Directed.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.5760 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.5762 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.5760 x._@.Mathlib.LinearAlgebra.Span._hyg.5762) S) -> (Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (iSup.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι S)) (Set.iUnion.{u1, u3} M ι (fun (i : ι) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (S i))))
+Case conversion may be inaccurate. Consider using '#align submodule.coe_supr_of_directed Submodule.coe_iSup_of_directedₓ'. -/
 @[simp]
-theorem coe_supᵢ_of_directed {ι} [hι : Nonempty ι] (S : ι → Submodule R M)
-    (H : Directed (· ≤ ·) S) : ((supᵢ S : Submodule R M) : Set M) = ⋃ i, S i :=
+theorem coe_iSup_of_directed {ι} [hι : Nonempty ι] (S : ι → Submodule R M)
+    (H : Directed (· ≤ ·) S) : ((iSup S : Submodule R M) : Set M) = ⋃ i, S i :=
   by
-  refine' subset.antisymm _ (Union_subset <| le_supᵢ S)
+  refine' subset.antisymm _ (Union_subset <| le_iSup S)
   suffices (span R (⋃ i, (S i : Set M)) : Set M) ⊆ ⋃ i : ι, ↑(S i) by
     simpa only [span_Union, span_eq] using this
   refine' fun x hx => span_induction hx (fun _ => id) _ _ _ <;> simp only [mem_Union, exists_imp]
@@ -535,45 +535,45 @@ theorem coe_supᵢ_of_directed {ι} [hι : Nonempty ι] (S : ι → Submodule R
     rcases H i j with ⟨k, ik, jk⟩
     exact ⟨k, add_mem (ik hi) (jk hj)⟩
   · exact fun a x i hi => ⟨i, smul_mem _ a hi⟩
-#align submodule.coe_supr_of_directed Submodule.coe_supᵢ_of_directed
+#align submodule.coe_supr_of_directed Submodule.coe_iSup_of_directed
 
-/- warning: submodule.mem_supr_of_directed -> Submodule.mem_supᵢ_of_directed is a dubious translation:
+/- warning: submodule.mem_supr_of_directed -> Submodule.mem_iSup_of_directed 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} [_inst_7 : Nonempty.{u3} ι] (S : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Directed.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) S) -> (forall {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι S)) (Exists.{u3} ι (fun (i : ι) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (S i))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} [_inst_7 : Nonempty.{u3} ι] (S : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Directed.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) S) -> (forall {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι S)) (Exists.{u3} ι (fun (i : ι) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (S i))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} [_inst_7 : Nonempty.{u3} ι] (S : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), (Directed.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.6058 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.6060 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.6058 x._@.Mathlib.LinearAlgebra.Span._hyg.6060) S) -> (forall {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι S)) (Exists.{u3} ι (fun (i : ι) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (S i))))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_of_directed Submodule.mem_supᵢ_of_directedₓ'. -/
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} [_inst_7 : Nonempty.{u3} ι] (S : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), (Directed.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.6058 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.6060 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.6058 x._@.Mathlib.LinearAlgebra.Span._hyg.6060) S) -> (forall {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (iSup.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι S)) (Exists.{u3} ι (fun (i : ι) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (S i))))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_of_directed Submodule.mem_iSup_of_directedₓ'. -/
 @[simp]
-theorem mem_supᵢ_of_directed {ι} [Nonempty ι] (S : ι → Submodule R M) (H : Directed (· ≤ ·) S) {x} :
-    x ∈ supᵢ S ↔ ∃ i, x ∈ S i :=
+theorem mem_iSup_of_directed {ι} [Nonempty ι] (S : ι → Submodule R M) (H : Directed (· ≤ ·) S) {x} :
+    x ∈ iSup S ↔ ∃ i, x ∈ S i :=
   by
   rw [← SetLike.mem_coe, coe_supr_of_directed S H, mem_Union]
   rfl
-#align submodule.mem_supr_of_directed Submodule.mem_supᵢ_of_directed
+#align submodule.mem_supr_of_directed Submodule.mem_iSup_of_directed
 
-/- warning: submodule.mem_Sup_of_directed -> Submodule.mem_supₛ_of_directed is a dubious translation:
+/- warning: submodule.mem_Sup_of_directed -> Submodule.mem_sSup_of_directed 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {z : M}, (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) s) -> (DirectedOn.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) s) -> (Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (SupSet.supₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) s)) (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (y : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Exists.{0} (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) (fun (H : Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z y))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {z : M}, (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) s) -> (DirectedOn.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) s) -> (Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (SupSet.sSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) s)) (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (y : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Exists.{0} (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) (fun (H : Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z y))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {z : M}, (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) s) -> (DirectedOn.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.6191 : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.6193 : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.6191 x._@.Mathlib.LinearAlgebra.Span._hyg.6193) s) -> (Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (SupSet.supₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) s)) (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (y : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => And (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z y))))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_Sup_of_directed Submodule.mem_supₛ_of_directedₓ'. -/
-theorem mem_supₛ_of_directed {s : Set (Submodule R M)} {z} (hs : s.Nonempty)
-    (hdir : DirectedOn (· ≤ ·) s) : z ∈ supₛ s ↔ ∃ y ∈ s, z ∈ y :=
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {z : M}, (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) s) -> (DirectedOn.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.6191 : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.6193 : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.6191 x._@.Mathlib.LinearAlgebra.Span._hyg.6193) s) -> (Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (SupSet.sSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) s)) (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (y : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => And (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z y))))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_Sup_of_directed Submodule.mem_sSup_of_directedₓ'. -/
+theorem mem_sSup_of_directed {s : Set (Submodule R M)} {z} (hs : s.Nonempty)
+    (hdir : DirectedOn (· ≤ ·) s) : z ∈ sSup s ↔ ∃ y ∈ s, z ∈ y :=
   by
   haveI : Nonempty s := hs.to_subtype
-  simp only [supₛ_eq_supᵢ', mem_supr_of_directed _ hdir.directed_coe, SetCoe.exists, Subtype.coe_mk]
-#align submodule.mem_Sup_of_directed Submodule.mem_supₛ_of_directed
+  simp only [sSup_eq_iSup', mem_supr_of_directed _ hdir.directed_coe, SetCoe.exists, Subtype.coe_mk]
+#align submodule.mem_Sup_of_directed Submodule.mem_sSup_of_directed
 
-/- warning: submodule.coe_supr_of_chain -> Submodule.coe_supᵢ_of_chain is a dubious translation:
+/- warning: submodule.coe_supr_of_chain -> Submodule.coe_iSup_of_chain 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (a : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))), Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (supᵢ.{u2, 1} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) Nat (fun (k : Nat) => coeFn.{succ u2, succ u2} (OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (fun (_x : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) => Nat -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (OrderHom.hasCoeToFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k))) (Set.unionᵢ.{u2, 1} M Nat (fun (k : Nat) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (coeFn.{succ u2, succ u2} (OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (fun (_x : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) => Nat -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (OrderHom.hasCoeToFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (a : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))), Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (iSup.{u2, 1} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) Nat (fun (k : Nat) => coeFn.{succ u2, succ u2} (OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (fun (_x : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) => Nat -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (OrderHom.hasCoeToFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k))) (Set.iUnion.{u2, 1} M Nat (fun (k : Nat) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (coeFn.{succ u2, succ u2} (OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (fun (_x : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) => Nat -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (OrderHom.hasCoeToFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (a : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (supᵢ.{u2, 1} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) Nat (fun (k : Nat) => OrderHom.toFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k))) (Set.unionᵢ.{u2, 1} M Nat (fun (k : Nat) => SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OrderHom.toFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k)))
-Case conversion may be inaccurate. Consider using '#align submodule.coe_supr_of_chain Submodule.coe_supᵢ_of_chainₓ'. -/
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (a : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (iSup.{u2, 1} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) Nat (fun (k : Nat) => OrderHom.toFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k))) (Set.iUnion.{u2, 1} M Nat (fun (k : Nat) => SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OrderHom.toFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k)))
+Case conversion may be inaccurate. Consider using '#align submodule.coe_supr_of_chain Submodule.coe_iSup_of_chainₓ'. -/
 @[norm_cast, simp]
-theorem coe_supᵢ_of_chain (a : ℕ →o Submodule R M) : (↑(⨆ k, a k) : Set M) = ⋃ k, (a k : Set M) :=
-  coe_supᵢ_of_directed a a.Monotone.directed_le
-#align submodule.coe_supr_of_chain Submodule.coe_supᵢ_of_chain
+theorem coe_iSup_of_chain (a : ℕ →o Submodule R M) : (↑(⨆ k, a k) : Set M) = ⋃ k, (a k : Set M) :=
+  coe_iSup_of_directed a a.Monotone.directed_le
+#align submodule.coe_supr_of_chain Submodule.coe_iSup_of_chain
 
 /- warning: submodule.coe_scott_continuous -> Submodule.coe_scott_continuous is a dubious translation:
 lean 3 declaration is
@@ -585,19 +585,19 @@ Case conversion may be inaccurate. Consider using '#align submodule.coe_scott_co
 Scott continuous for the ω-complete partial order induced by the complete lattice structures. -/
 theorem coe_scott_continuous :
     OmegaCompletePartialOrder.Continuous' (coe : Submodule R M → Set M) :=
-  ⟨SetLike.coe_mono, coe_supᵢ_of_chain⟩
+  ⟨SetLike.coe_mono, coe_iSup_of_chain⟩
 #align submodule.coe_scott_continuous Submodule.coe_scott_continuous
 
-/- warning: submodule.mem_supr_of_chain -> Submodule.mem_supᵢ_of_chain is a dubious translation:
+/- warning: submodule.mem_supr_of_chain -> Submodule.mem_iSup_of_chain 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (a : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (m : M), Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u2, 1} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) Nat (fun (k : Nat) => coeFn.{succ u2, succ u2} (OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (fun (_x : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) => Nat -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (OrderHom.hasCoeToFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k))) (Exists.{1} Nat (fun (k : Nat) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (coeFn.{succ u2, succ u2} (OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (fun (_x : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) => Nat -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (OrderHom.hasCoeToFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (a : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (m : M), Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (iSup.{u2, 1} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) Nat (fun (k : Nat) => coeFn.{succ u2, succ u2} (OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (fun (_x : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) => Nat -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (OrderHom.hasCoeToFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k))) (Exists.{1} Nat (fun (k : Nat) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (coeFn.{succ u2, succ u2} (OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (fun (_x : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) => Nat -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (OrderHom.hasCoeToFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (a : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (m : M), Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u2, 1} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) Nat (fun (k : Nat) => OrderHom.toFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k))) (Exists.{1} Nat (fun (k : Nat) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (OrderHom.toFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k)))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_of_chain Submodule.mem_supᵢ_of_chainₓ'. -/
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (a : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (m : M), Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (iSup.{u2, 1} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) Nat (fun (k : Nat) => OrderHom.toFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k))) (Exists.{1} Nat (fun (k : Nat) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (OrderHom.toFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k)))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_of_chain Submodule.mem_iSup_of_chainₓ'. -/
 @[simp]
-theorem mem_supᵢ_of_chain (a : ℕ →o Submodule R M) (m : M) : (m ∈ ⨆ k, a k) ↔ ∃ k, m ∈ a k :=
-  mem_supᵢ_of_directed a a.Monotone.directed_le
-#align submodule.mem_supr_of_chain Submodule.mem_supᵢ_of_chain
+theorem mem_iSup_of_chain (a : ℕ →o Submodule R M) (m : M) : (m ∈ ⨆ k, a k) ↔ ∃ k, m ∈ a k :=
+  mem_iSup_of_directed a a.Monotone.directed_le
+#align submodule.mem_supr_of_chain Submodule.mem_iSup_of_chain
 
 section
 
@@ -1045,38 +1045,38 @@ theorem not_mem_span_of_apply_not_mem_span_image [RingHomSurjective σ₁₂] (f
   h.imp (apply_mem_span_image_of_mem_span f)
 #align submodule.not_mem_span_of_apply_not_mem_span_image Submodule.not_mem_span_of_apply_not_mem_span_image
 
-/- warning: submodule.supr_span -> Submodule.supᵢ_span is a dubious translation:
+/- warning: submodule.supr_span -> Submodule.iSup_span 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Set.{u2} M)), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (p i))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.unionᵢ.{u2, u3} M ι (fun (i : ι) => p i)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Set.{u2} M)), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (p i))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.iUnion.{u2, u3} M ι (fun (i : ι) => p i)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Set.{u2} M)), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (p i))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.unionᵢ.{u2, u3} M ι (fun (i : ι) => p i)))
-Case conversion may be inaccurate. Consider using '#align submodule.supr_span Submodule.supᵢ_spanₓ'. -/
-theorem supᵢ_span {ι : Sort _} (p : ι → Set M) : (⨆ i, span R (p i)) = span R (⋃ i, p i) :=
-  le_antisymm (supᵢ_le fun i => span_mono <| subset_unionᵢ _ i) <|
-    span_le.mpr <| unionᵢ_subset fun i m hm => mem_supᵢ_of_mem i <| subset_span hm
-#align submodule.supr_span Submodule.supᵢ_span
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Set.{u2} M)), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (p i))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.iUnion.{u2, u3} M ι (fun (i : ι) => p i)))
+Case conversion may be inaccurate. Consider using '#align submodule.supr_span Submodule.iSup_spanₓ'. -/
+theorem iSup_span {ι : Sort _} (p : ι → Set M) : (⨆ i, span R (p i)) = span R (⋃ i, p i) :=
+  le_antisymm (iSup_le fun i => span_mono <| subset_iUnion _ i) <|
+    span_le.mpr <| iUnion_subset fun i m hm => mem_iSup_of_mem i <| subset_span hm
+#align submodule.supr_span Submodule.iSup_span
 
-/- warning: submodule.supr_eq_span -> Submodule.supᵢ_eq_span is a dubious translation:
+/- warning: submodule.supr_eq_span -> Submodule.iSup_eq_span 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.unionᵢ.{u2, u3} M ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (p i))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.iUnion.{u2, u3} M ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (p i))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Set.unionᵢ.{u1, u3} M ι (fun (i : ι) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (p i))))
-Case conversion may be inaccurate. Consider using '#align submodule.supr_eq_span Submodule.supᵢ_eq_spanₓ'. -/
-theorem supᵢ_eq_span {ι : Sort _} (p : ι → Submodule R M) : (⨆ i, p i) = span R (⋃ i, ↑(p i)) := by
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (iSup.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Set.iUnion.{u1, u3} M ι (fun (i : ι) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (p i))))
+Case conversion may be inaccurate. Consider using '#align submodule.supr_eq_span Submodule.iSup_eq_spanₓ'. -/
+theorem iSup_eq_span {ι : Sort _} (p : ι → Submodule R M) : (⨆ i, p i) = span R (⋃ i, ↑(p i)) := by
   simp_rw [← supr_span, span_eq]
-#align submodule.supr_eq_span Submodule.supᵢ_eq_span
+#align submodule.supr_eq_span Submodule.iSup_eq_span
 
-/- warning: submodule.supr_to_add_submonoid -> Submodule.supᵢ_toAddSubmonoid is a dubious translation:
+/- warning: submodule.supr_to_add_submonoid -> Submodule.iSup_toAddSubmonoid 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (supᵢ.{u2, u3} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (ConditionallyCompleteLattice.toHasSup.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (CompleteLattice.toConditionallyCompleteLattice.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (AddSubmonoid.completeLattice.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) ι (fun (i : ι) => Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (p i)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (iSup.{u2, u3} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (ConditionallyCompleteLattice.toHasSup.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (CompleteLattice.toConditionallyCompleteLattice.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (AddSubmonoid.completeLattice.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) ι (fun (i : ι) => Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (p i)))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), Eq.{succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))) (Submodule.toAddSubmonoid.{u2, u1} R M _inst_1 _inst_2 _inst_3 (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (supᵢ.{u1, u3} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))) (ConditionallyCompleteLattice.toSupSet.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))) (CompleteLattice.toConditionallyCompleteLattice.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) ι (fun (i : ι) => Submodule.toAddSubmonoid.{u2, u1} R M _inst_1 _inst_2 _inst_3 (p i)))
-Case conversion may be inaccurate. Consider using '#align submodule.supr_to_add_submonoid Submodule.supᵢ_toAddSubmonoidₓ'. -/
-theorem supᵢ_toAddSubmonoid {ι : Sort _} (p : ι → Submodule R M) :
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), Eq.{succ u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))) (Submodule.toAddSubmonoid.{u2, u1} R M _inst_1 _inst_2 _inst_3 (iSup.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (iSup.{u1, u3} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))) (ConditionallyCompleteLattice.toSupSet.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))) (CompleteLattice.toConditionallyCompleteLattice.{u1} (AddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) ι (fun (i : ι) => Submodule.toAddSubmonoid.{u2, u1} R M _inst_1 _inst_2 _inst_3 (p i)))
+Case conversion may be inaccurate. Consider using '#align submodule.supr_to_add_submonoid Submodule.iSup_toAddSubmonoidₓ'. -/
+theorem iSup_toAddSubmonoid {ι : Sort _} (p : ι → Submodule R M) :
     (⨆ i, p i).toAddSubmonoid = ⨆ i, (p i).toAddSubmonoid :=
   by
-  refine' le_antisymm (fun x => _) (supᵢ_le fun i => to_add_submonoid_mono <| le_supᵢ _ i)
-  simp_rw [supr_eq_span, AddSubmonoid.supᵢ_eq_closure, mem_to_add_submonoid, coe_to_add_submonoid]
+  refine' le_antisymm (fun x => _) (iSup_le fun i => to_add_submonoid_mono <| le_iSup _ i)
+  simp_rw [supr_eq_span, AddSubmonoid.iSup_eq_closure, mem_to_add_submonoid, coe_to_add_submonoid]
   intro hx
   refine' Submodule.span_induction hx (fun x hx => _) _ (fun x y hx hy => _) fun r x hx => _
   · exact AddSubmonoid.subset_closure hx
@@ -1091,36 +1091,36 @@ theorem supᵢ_toAddSubmonoid {ι : Sort _} (p : ι → Submodule R M) :
     · intro x y hx hy
       rw [smul_add]
       exact AddSubmonoid.add_mem _ hx hy
-#align submodule.supr_to_add_submonoid Submodule.supᵢ_toAddSubmonoid
+#align submodule.supr_to_add_submonoid Submodule.iSup_toAddSubmonoid
 
-/- warning: submodule.supr_induction -> Submodule.supᵢ_induction is a dubious translation:
+/- warning: submodule.supr_induction -> Submodule.iSup_induction 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) {C : M -> Prop} {x : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> (forall (i : ι) (x : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (p i)) -> (C x)) -> (C (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))))))) -> (forall (x : M) (y : M), (C x) -> (C y) -> (C (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)))) x y))) -> (C x)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) {C : M -> Prop} {x : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> (forall (i : ι) (x : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (p i)) -> (C x)) -> (C (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))))))) -> (forall (x : M) (y : M), (C x) -> (C y) -> (C (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)))) x y))) -> (C x)
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) {C : M -> Prop} {x : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> (forall (i : ι) (x : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (p i)) -> (C x)) -> (C (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) -> (forall (x : M) (y : M), (C x) -> (C y) -> (C (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)))) x y))) -> (C x)
-Case conversion may be inaccurate. Consider using '#align submodule.supr_induction Submodule.supᵢ_inductionₓ'. -/
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) {C : M -> Prop} {x : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (iSup.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> (forall (i : ι) (x : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (p i)) -> (C x)) -> (C (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) -> (forall (x : M) (y : M), (C x) -> (C y) -> (C (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)))) x y))) -> (C x)
+Case conversion may be inaccurate. Consider using '#align submodule.supr_induction Submodule.iSup_inductionₓ'. -/
 /-- An induction principle for elements of `⨆ i, p i`.
 If `C` holds for `0` and all elements of `p i` for all `i`, and is preserved under addition,
 then it holds for all elements of the supremum of `p`. -/
 @[elab_as_elim]
-theorem supᵢ_induction {ι : Sort _} (p : ι → Submodule R M) {C : M → Prop} {x : M}
+theorem iSup_induction {ι : Sort _} (p : ι → Submodule R M) {C : M → Prop} {x : M}
     (hx : x ∈ ⨆ i, p i) (hp : ∀ (i), ∀ x ∈ p i, C x) (h0 : C 0)
     (hadd : ∀ x y, C x → C y → C (x + y)) : C x :=
   by
   rw [← mem_to_add_submonoid, supr_to_add_submonoid] at hx
-  exact AddSubmonoid.supᵢ_induction _ hx hp h0 hadd
-#align submodule.supr_induction Submodule.supᵢ_induction
+  exact AddSubmonoid.iSup_induction _ hx hp h0 hadd
+#align submodule.supr_induction Submodule.iSup_induction
 
-/- warning: submodule.supr_induction' -> Submodule.supᵢ_induction' is a dubious translation:
+/- warning: submodule.supr_induction' -> Submodule.iSup_induction' 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) {C : forall (x : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> Prop}, (forall (i : ι) (x : M) (H : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (p i)), C x (Submodule.mem_supᵢ_of_mem.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 ι x (fun (i : ι) => p i) i H)) -> (C (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)))))) (ZeroMemClass.zero_mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (AddSubmonoidClass.to_zeroMemClass.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)))) -> (forall (x : M) (y : M) (hx : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (hy : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))), (C x hx) -> (C y hy) -> (C (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)))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)) x y hx hy))) -> (forall {x : M} (hx : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))), C x hx)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) {C : forall (x : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> Prop}, (forall (i : ι) (x : M) (H : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (p i)), C x (Submodule.mem_iSup_of_mem.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 ι x (fun (i : ι) => p i) i H)) -> (C (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)))))) (ZeroMemClass.zero_mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (AddSubmonoidClass.to_zeroMemClass.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)))) -> (forall (x : M) (y : M) (hx : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (hy : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))), (C x hx) -> (C y hy) -> (C (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)))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)) x y hx hy))) -> (forall {x : M} (hx : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))), C x hx)
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) {C : forall (x : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> Prop}, (forall (i : ι) (x : M) (H : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (p i)), C x (Submodule.mem_supᵢ_of_mem.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 ι x (fun (i : ι) => p i) i H)) -> (C (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)))) (ZeroMemClass.zero_mem.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (AddSubmonoidClass.toZeroMemClass.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.addSubmonoidClass.{u2, u1} R M _inst_1 _inst_2 _inst_3)) (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)))) -> (forall (x : M) (y : M) (hx : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (hy : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) y (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))), (C x hx) -> (C y hy) -> (C (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)))) x y) (AddMemClass.add_mem.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))) (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (AddSubmonoidClass.toAddMemClass.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.addSubmonoidClass.{u2, u1} R M _inst_1 _inst_2 _inst_3)) (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)) x y hx hy))) -> (forall {x : M} (hx : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))), C x hx)
-Case conversion may be inaccurate. Consider using '#align submodule.supr_induction' Submodule.supᵢ_induction'ₓ'. -/
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) {C : forall (x : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (iSup.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> Prop}, (forall (i : ι) (x : M) (H : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (p i)), C x (Submodule.mem_iSup_of_mem.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 ι x (fun (i : ι) => p i) i H)) -> (C (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)))) (ZeroMemClass.zero_mem.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (AddSubmonoidClass.toZeroMemClass.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.addSubmonoidClass.{u2, u1} R M _inst_1 _inst_2 _inst_3)) (iSup.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)))) -> (forall (x : M) (y : M) (hx : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (iSup.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (hy : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) y (iSup.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))), (C x hx) -> (C y hy) -> (C (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)))) x y) (AddMemClass.add_mem.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))) (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (AddSubmonoidClass.toAddMemClass.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.addSubmonoidClass.{u2, u1} R M _inst_1 _inst_2 _inst_3)) (iSup.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)) x y hx hy))) -> (forall {x : M} (hx : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (iSup.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))), C x hx)
+Case conversion may be inaccurate. Consider using '#align submodule.supr_induction' Submodule.iSup_induction'ₓ'. -/
 /-- A dependent version of `submodule.supr_induction`. -/
 @[elab_as_elim]
-theorem supᵢ_induction' {ι : Sort _} (p : ι → Submodule R M) {C : ∀ x, (x ∈ ⨆ i, p i) → Prop}
-    (hp : ∀ (i), ∀ x ∈ p i, C x (mem_supᵢ_of_mem i ‹_›)) (h0 : C 0 (zero_mem _))
+theorem iSup_induction' {ι : Sort _} (p : ι → Submodule R M) {C : ∀ x, (x ∈ ⨆ i, p i) → Prop}
+    (hp : ∀ (i), ∀ x ∈ p i, C x (mem_iSup_of_mem i ‹_›)) (h0 : C 0 (zero_mem _))
     (hadd : ∀ x y hx hy, C x hx → C y hy → C (x + y) (add_mem ‹_› ‹_›)) {x : M}
     (hx : x ∈ ⨆ i, p i) : C x hx :=
   by
@@ -1130,7 +1130,7 @@ theorem supᵢ_induction' {ι : Sort _} (p : ι → Submodule R M) {C : ∀ x, (
   · exact ⟨_, h0⟩
   · rintro ⟨_, Cx⟩ ⟨_, Cy⟩
     refine' ⟨_, hadd _ _ _ _ Cx Cy⟩
-#align submodule.supr_induction' Submodule.supᵢ_induction'
+#align submodule.supr_induction' Submodule.iSup_induction'
 
 /- warning: submodule.span_singleton_le_iff_mem -> Submodule.span_singleton_le_iff_mem is a dubious translation:
 lean 3 declaration is
@@ -1147,7 +1147,7 @@ theorem span_singleton_le_iff_mem (m : M) (p : Submodule R M) : (R ∙ m) ≤ p
 theorem singleton_span_isCompactElement (x : M) :
     CompleteLattice.IsCompactElement (span R {x} : Submodule R M) :=
   by
-  rw [CompleteLattice.isCompactElement_iff_le_of_directed_supₛ_le]
+  rw [CompleteLattice.isCompactElement_iff_le_of_directed_sSup_le]
   intro d hemp hdir hsup
   have : x ∈ Sup d := (set_like.le_def.mp hsup) (mem_span_singleton_self x)
   obtain ⟨y, ⟨hyd, hxy⟩⟩ := (mem_Sup_of_directed hemp hdir).mp this
@@ -1162,7 +1162,7 @@ theorem finset_span_isCompactElement (S : Finset M) :
   by
   rw [span_eq_supr_of_singleton_spans]
   simp only [Finset.mem_coe]
-  rw [← Finset.sup_eq_supᵢ]
+  rw [← Finset.sup_eq_iSup]
   exact
     CompleteLattice.finset_sup_compact_of_compact S fun x _ => singleton_span_is_compact_element x
 #align submodule.finset_span_is_compact_element Submodule.finset_span_isCompactElement
@@ -1182,17 +1182,17 @@ instance : IsCompactlyGenerated (Submodule R M) :=
       ⟨fun t ht => by
         rcases(Set.mem_image _ _ _).1 ht with ⟨x, hx, rfl⟩
         apply singleton_span_is_compact_element, by
-        rw [supₛ_eq_supᵢ, supᵢ_image, ← span_eq_supr_of_singleton_spans, span_eq]⟩⟩⟩
+        rw [sSup_eq_iSup, iSup_image, ← span_eq_supr_of_singleton_spans, span_eq]⟩⟩⟩
 
-/- warning: submodule.submodule_eq_Sup_le_nonzero_spans -> Submodule.submodule_eq_supₛ_le_nonzero_spans is a dubious translation:
+/- warning: submodule.submodule_eq_Sup_le_nonzero_spans -> Submodule.submodule_eq_sSup_le_nonzero_spans 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p (SupSet.supₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (setOf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (T : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Exists.{succ u2} M (fun (m : M) => Exists.{0} (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m p) (fun (hm : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m p) => Exists.{0} (Ne.{succ u2} M m (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))))))) (fun (hz : Ne.{succ u2} M m (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 u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) T (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) m))))))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p (SupSet.sSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (setOf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (T : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Exists.{succ u2} M (fun (m : M) => Exists.{0} (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m p) (fun (hm : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m p) => Exists.{0} (Ne.{succ u2} M m (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))))))) (fun (hz : Ne.{succ u2} M m (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 u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) T (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) m))))))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] (p : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) p (SupSet.supₛ.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) (setOf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (T : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Exists.{succ u1} M (fun (m : M) => Exists.{0} (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m p) (fun (hm : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m p) => Exists.{0} (Ne.{succ u1} M m (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) (fun (hz : Ne.{succ u1} M m (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) => Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) T (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) m))))))))
-Case conversion may be inaccurate. Consider using '#align submodule.submodule_eq_Sup_le_nonzero_spans Submodule.submodule_eq_supₛ_le_nonzero_spansₓ'. -/
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] (p : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) p (SupSet.sSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) (setOf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (T : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Exists.{succ u1} M (fun (m : M) => Exists.{0} (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m p) (fun (hm : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m p) => Exists.{0} (Ne.{succ u1} M m (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) (fun (hz : Ne.{succ u1} M m (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) => Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) T (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) m))))))))
+Case conversion may be inaccurate. Consider using '#align submodule.submodule_eq_Sup_le_nonzero_spans Submodule.submodule_eq_sSup_le_nonzero_spansₓ'. -/
 /-- A submodule is equal to the supremum of the spans of the submodule's nonzero elements. -/
-theorem submodule_eq_supₛ_le_nonzero_spans (p : Submodule R M) :
-    p = supₛ { T : Submodule R M | ∃ (m : M)(hm : m ∈ p)(hz : m ≠ 0), T = span R {m} } :=
+theorem submodule_eq_sSup_le_nonzero_spans (p : Submodule R M) :
+    p = sSup { T : Submodule R M | ∃ (m : M)(hm : m ∈ p)(hz : m ≠ 0), T = span R {m} } :=
   by
   let S := { T : Submodule R M | ∃ (m : M)(hm : m ∈ p)(hz : m ≠ 0), T = span R {m} }
   apply le_antisymm
@@ -1200,11 +1200,11 @@ theorem submodule_eq_supₛ_le_nonzero_spans (p : Submodule R M) :
     by_cases h : m = 0
     · rw [h]
       simp
-    · exact @le_supₛ _ _ S _ ⟨m, ⟨hm, ⟨h, rfl⟩⟩⟩ m (mem_span_singleton_self m)
-  · rw [supₛ_le_iff]
+    · exact @le_sSup _ _ S _ ⟨m, ⟨hm, ⟨h, rfl⟩⟩⟩ m (mem_span_singleton_self m)
+  · rw [sSup_le_iff]
     rintro S ⟨_, ⟨_, ⟨_, rfl⟩⟩⟩
     rwa [span_singleton_le_iff_mem]
-#align submodule.submodule_eq_Sup_le_nonzero_spans Submodule.submodule_eq_supₛ_le_nonzero_spans
+#align submodule.submodule_eq_Sup_le_nonzero_spans Submodule.submodule_eq_sSup_le_nonzero_spans
 
 /- warning: submodule.lt_sup_iff_not_mem -> Submodule.lt_sup_iff_not_mem is a dubious translation:
 lean 3 declaration is
@@ -1236,18 +1236,18 @@ theorem lt_sup_iff_not_mem {I : Submodule R M} {a : M} : (I < I ⊔ R ∙ a) ↔
       exact this (mem_span_singleton_self a)
 #align submodule.lt_sup_iff_not_mem Submodule.lt_sup_iff_not_mem
 
-/- warning: submodule.mem_supr -> Submodule.mem_supᵢ is a dubious translation:
+/- warning: submodule.mem_supr -> Submodule.mem_iSup 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) {m : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (forall (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (forall (i : ι), LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (p i) N) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m N))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) {m : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (iSup.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (forall (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (forall (i : ι), LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (p i) N) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m N))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) {m : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (forall (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), (forall (i : ι), LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (p i) N) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m N))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_supr Submodule.mem_supᵢₓ'. -/
-theorem mem_supᵢ {ι : Sort _} (p : ι → Submodule R M) {m : M} :
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) {m : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (iSup.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (forall (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), (forall (i : ι), LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (p i) N) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m N))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_supr Submodule.mem_iSupₓ'. -/
+theorem mem_iSup {ι : Sort _} (p : ι → Submodule R M) {m : M} :
     (m ∈ ⨆ i, p i) ↔ ∀ N, (∀ i, p i ≤ N) → m ∈ N :=
   by
-  rw [← span_singleton_le_iff_mem, le_supᵢ_iff]
+  rw [← span_singleton_le_iff_mem, le_iSup_iff]
   simp only [span_singleton_le_iff_mem]
-#align submodule.mem_supr Submodule.mem_supᵢ
+#align submodule.mem_supr Submodule.mem_iSup
 
 section
 

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

@@ -1669,7 +1669,7 @@ open Classical
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (f : LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) {x : V}, (Ne.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) => V -> K) (LinearMap.hasCoeToFun.{u1, u1, u2, u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f x) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)) (LinearMap.ker.{u1, u1, u2, u1, max u2 u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.semilinearMapClass.{u1, u1, u2, u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f)) (Top.top.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))
 but is expected to have type
-  forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] (f : LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) {x : V}, (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (CommGroupWithZero.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (Semifield.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) _inst_1))))))) -> (Eq.{succ u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Sup.sup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Submodule.span.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3 (Singleton.singleton.{u1, u1} V (Set.{u1} V) (Set.instSingletonSet.{u1} V) x)) (LinearMap.ker.{u2, u2, u1, u2, max u2 u1} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))))) (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) f)) (Top.top.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3)))
+  forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] (f : LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) {x : V}, (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (CommGroupWithZero.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (Semifield.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) _inst_1))))))) -> (Eq.{succ u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Sup.sup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Submodule.span.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3 (Singleton.singleton.{u1, u1} V (Set.{u1} V) (Set.instSingletonSet.{u1} V) x)) (LinearMap.ker.{u2, u2, u1, u2, max u2 u1} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f)) (Top.top.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3)))
 Case conversion may be inaccurate. Consider using '#align linear_map.span_singleton_sup_ker_eq_top LinearMap.span_singleton_sup_ker_eq_topₓ'. -/
 theorem span_singleton_sup_ker_eq_top (f : V →ₗ[K] K) {x : V} (hx : f x ≠ 0) :
     (K ∙ x) ⊔ f.ker = ⊤ :=
@@ -1726,7 +1726,7 @@ variable (K V) [Field K] [AddCommGroup V] [Module K V]
 lean 3 declaration is
   forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (LinearEquiv.{u1, u1, u1, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} K _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} K _inst_1) K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))
+  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.to_span_nonzero_singleton LinearEquiv.toSpanNonzeroSingletonₓ'. -/
 /-- Given a nonzero element `x` of a vector space `V` over a field `K`, the natural
     map from `K` to the span of `x`, with invertibility check to consider it as an
@@ -1742,7 +1742,7 @@ def toSpanNonzeroSingleton (x : V) (h : x ≠ 0) : K ≃ₗ[K] K ∙ x :=
 lean 3 declaration is
   forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, u1, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} K _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} K _inst_1) K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)))) (fun (_x : LinearEquiv.{u1, u1, u1, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} K _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} K _inst_1) K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K 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K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)))) => K -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)))) (LinearEquiv.hasCoeToFun.{u1, u1, u1, u2} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K 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(NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} K _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} K _inst_1)) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.Mem.{u2, u2} V (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K 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(DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u2, max u1 u2} K K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u2} K K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))
+  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u2, max u1 u2} K K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u2} K K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.to_span_nonzero_singleton_one LinearEquiv.toSpanNonzeroSingleton_oneₓ'. -/
 theorem toSpanNonzeroSingleton_one (x : V) (h : x ≠ 0) :
     LinearEquiv.toSpanNonzeroSingleton K V x h 1 =
@@ -1757,7 +1757,7 @@ theorem toSpanNonzeroSingleton_one (x : V) (h : x ≠ 0) :
 lean 3 declaration is
   forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) K (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))
+  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.coord LinearEquiv.coordₓ'. -/
 /-- Given a nonzero element `x` of a vector space `V` over a field `K`, the natural map
     from the span of `x` to `K`.-/
@@ -1769,7 +1769,7 @@ abbrev coord (x : V) (h : x ≠ 0) : (K ∙ x) ≃ₗ[K] K :=
 lean 3 declaration is
   forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))), Eq.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) K (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) K (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) => 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(Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1)) (LinearEquiv.coord.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.Mem.{u2, u2} V (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K 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(DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (fun (_x : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u1, max u1 u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K 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(AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) 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(Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (NonAssocRing.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V 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(DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) 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(Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) _inst_1))))))
+  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K 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(DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (fun (_x : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u1, max u1 u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u1, max u1 u2} K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearEquiv.coord.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) 1 (One.toOfNat1.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K 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K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V 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V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.coord_self LinearEquiv.coord_selfₓ'. -/
 theorem coord_self (x : V) (h : x ≠ 0) :
     (coord K V x h) (⟨x, Submodule.mem_span_singleton_self x⟩ : K ∙ x) = 1 := by

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

@@ -1669,7 +1669,7 @@ open Classical
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (f : LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) {x : V}, (Ne.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) => V -> K) (LinearMap.hasCoeToFun.{u1, u1, u2, u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f x) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)) (LinearMap.ker.{u1, u1, u2, u1, max u2 u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.semilinearMapClass.{u1, u1, u2, u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f)) (Top.top.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))
 but is expected to have type
-  forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] (f : LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1)) {x : V}, (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1)) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (CommGroupWithZero.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (Semifield.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) _inst_1))))))) -> (Eq.{succ u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Sup.sup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Submodule.span.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3 (Singleton.singleton.{u1, u1} V (Set.{u1} V) (Set.instSingletonSet.{u1} V) x)) (LinearMap.ker.{u2, u2, u1, u2, max u2 u1} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f)) (Top.top.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3)))
+  forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] (f : LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) {x : V}, (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (CommGroupWithZero.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (Semifield.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) _inst_1))))))) -> (Eq.{succ u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Sup.sup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Submodule.span.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3 (Singleton.singleton.{u1, u1} V (Set.{u1} V) (Set.instSingletonSet.{u1} V) x)) (LinearMap.ker.{u2, u2, u1, u2, max u2 u1} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))))) (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) _inst_3 (Semiring.toModule.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))) (RingHom.id.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_1)))))) f)) (Top.top.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3)))
 Case conversion may be inaccurate. Consider using '#align linear_map.span_singleton_sup_ker_eq_top LinearMap.span_singleton_sup_ker_eq_topₓ'. -/
 theorem span_singleton_sup_ker_eq_top (f : V →ₗ[K] K) {x : V} (hx : f x ≠ 0) :
     (K ∙ x) ⊔ f.ker = ⊤ :=
@@ -1726,7 +1726,7 @@ variable (K V) [Field K] [AddCommGroup V] [Module K V]
 lean 3 declaration is
   forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (LinearEquiv.{u1, u1, u1, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} K _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} K _inst_1) K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))
+  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.to_span_nonzero_singleton LinearEquiv.toSpanNonzeroSingletonₓ'. -/
 /-- Given a nonzero element `x` of a vector space `V` over a field `K`, the natural
     map from `K` to the span of `x`, with invertibility check to consider it as an
@@ -1742,7 +1742,7 @@ def toSpanNonzeroSingleton (x : V) (h : x ≠ 0) : K ≃ₗ[K] K ∙ x :=
 lean 3 declaration is
   forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, u1, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} K _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} K _inst_1) K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)))) (fun (_x : LinearEquiv.{u1, u1, u1, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} K _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} K _inst_1) K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K 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K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)))) => K -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)))) (LinearEquiv.hasCoeToFun.{u1, u1, u1, u2} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} K _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} K _inst_1)) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.Mem.{u2, u2} V (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1))))) (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K 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(DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K 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(Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u2} K K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))
+  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u2, max u1 u2} K K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u2} K K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (NonAssocRing.toOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.to_span_nonzero_singleton_one LinearEquiv.toSpanNonzeroSingleton_oneₓ'. -/
 theorem toSpanNonzeroSingleton_one (x : V) (h : x ≠ 0) :
     LinearEquiv.toSpanNonzeroSingleton K V x h 1 =
@@ -1757,7 +1757,7 @@ theorem toSpanNonzeroSingleton_one (x : V) (h : x ≠ 0) :
 lean 3 declaration is
   forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) K (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1))
+  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.coord LinearEquiv.coordₓ'. -/
 /-- Given a nonzero element `x` of a vector space `V` over a field `K`, the natural map
     from the span of `x` to `K`.-/
@@ -1769,7 +1769,7 @@ abbrev coord (x : V) (h : x ≠ 0) : (K ∙ x) ≃ₗ[K] K :=
 lean 3 declaration is
   forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))), Eq.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) K (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) K (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) => 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(Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1)) (LinearEquiv.coord.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.Mem.{u2, u2} V (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K 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(Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (fun (_x : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u1, max u1 u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} 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(Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (Semiring.toOne.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V 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(AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) 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(Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) _inst_1))))))
+  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K 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(DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (fun (_x : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u1, max u1 u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u1, max u1 u2} K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Semiring.toModule.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u1} K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V 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 Case conversion may be inaccurate. Consider using '#align linear_equiv.coord_self LinearEquiv.coord_selfₓ'. -/
 theorem coord_self (x : V) (h : x ≠ 0) :
     (coord K V x h) (⟨x, Submodule.mem_span_singleton_self x⟩ : K ∙ x) = 1 := by

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

@@ -1740,7 +1740,7 @@ def toSpanNonzeroSingleton (x : V) (h : x ≠ 0) : K ≃ₗ[K] K ∙ x :=
 
 /- warning: linear_equiv.to_span_nonzero_singleton_one -> LinearEquiv.toSpanNonzeroSingleton_one is a dubious translation:
 lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))
+  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, u1, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) 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(AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)))) (fun (_x : LinearEquiv.{u1, u1, u1, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} K _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} K _inst_1) K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)))) => K -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)))) (LinearEquiv.hasCoeToFun.{u1, u1, u1, u2} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} K _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} K _inst_1)) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.Mem.{u2, u2} V (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))
 but is expected to have type
   forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1))))) (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u2, max u1 u2} K K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u2} K K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.to_span_nonzero_singleton_one LinearEquiv.toSpanNonzeroSingleton_oneₓ'. -/
@@ -1767,7 +1767,7 @@ abbrev coord (x : V) (h : x ≠ 0) : (K ∙ x) ≃ₗ[K] K :=
 
 /- warning: linear_equiv.coord_self -> LinearEquiv.coord_self is a dubious translation:
 lean 3 declaration is
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))), Eq.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 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(Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1)) (LinearEquiv.coord.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.Mem.{u2, u2} V (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (AddCommGroupWithOne.toAddGroupWithOne.{u1} K (Ring.toAddCommGroupWithOne.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))
 but is expected to have type
   forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (fun (_x : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u1, max u1 u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u1, max u1 u2} K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K 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_inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.coord_self LinearEquiv.coord_selfₓ'. -/

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

@@ -62,30 +62,22 @@ end
 
 variable {s t : Set M}
 
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-Case conversion may be inaccurate. Consider using '#align submodule.mem_span Submodule.mem_spanₓ'. -/
+#print Submodule.mem_span /-
 theorem mem_span : x ∈ span R s ↔ ∀ p : Submodule R M, s ⊆ p → x ∈ p :=
   mem_interᵢ₂
 #align submodule.mem_span Submodule.mem_span
+-/
 
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-Case conversion may be inaccurate. Consider using '#align submodule.subset_span Submodule.subset_spanₓ'. -/
+#print Submodule.subset_span /-
 theorem subset_span : s ⊆ span R s := fun x h => mem_span.2 fun p hp => hp h
 #align submodule.subset_span Submodule.subset_span
+-/
 
 /- warning: submodule.span_le -> Submodule.span_le is a dubious translation:
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 but is expected to have type
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+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Set.{u1} M} {p : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3}, Iff (LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 s) p) (HasSubset.Subset.{u1} (Set.{u1} M) (Set.instHasSubsetSet.{u1} M) s (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) p))
 Case conversion may be inaccurate. Consider using '#align submodule.span_le Submodule.span_leₓ'. -/
 theorem span_le {p} : span R s ≤ p ↔ s ⊆ p :=
   ⟨Subset.trans subset_span, fun ss x h => mem_span.1 h _ ss⟩
@@ -114,37 +106,29 @@ theorem span_monotone : Monotone (span R : Set M → Submodule R M) := fun _ _ =
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, (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 _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p)) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) p)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, (HasSubset.Subset.{u2} (Set.{u2} M) (Set.instHasSubsetSet.{u2} M) s (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p)) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) p)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, (HasSubset.Subset.{u2} (Set.{u2} M) (Set.instHasSubsetSet.{u2} M) s (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) p)) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) p)
 Case conversion may be inaccurate. Consider using '#align submodule.span_eq_of_le Submodule.span_eq_of_leₓ'. -/
 theorem span_eq_of_le (h₁ : s ⊆ p) (h₂ : p ≤ span R s) : span R s = p :=
   le_antisymm (span_le.2 h₁) h₂
 #align submodule.span_eq_of_le Submodule.span_eq_of_le
 
-/- warning: submodule.span_eq -> Submodule.span_eq is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align submodule.span_eq Submodule.span_eqₓ'. -/
+#print Submodule.span_eq /-
 theorem span_eq : span R (p : Set M) = p :=
   span_eq_of_le _ (Subset.refl _) subset_span
 #align submodule.span_eq Submodule.span_eq
+-/
 
-/- warning: submodule.span_eq_span -> Submodule.span_eq_span is a dubious translation:
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-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M} {t : Set.{u2} M}, (HasSubset.Subset.{u2} (Set.{u2} M) (Set.instHasSubsetSet.{u2} M) s (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 t))) -> (HasSubset.Subset.{u2} (Set.{u2} M) (Set.instHasSubsetSet.{u2} M) t (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 t))
-Case conversion may be inaccurate. Consider using '#align submodule.span_eq_span Submodule.span_eq_spanₓ'. -/
+#print Submodule.span_eq_span /-
 theorem span_eq_span (hs : s ⊆ span R t) (ht : t ⊆ span R s) : span R s = span R t :=
   le_antisymm (span_le.2 hs) (span_le.2 ht)
 #align submodule.span_eq_span Submodule.span_eq_span
+-/
 
 /- warning: submodule.span_coe_eq_restrict_scalars -> Submodule.span_coe_eq_restrictScalars is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {S : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) [_inst_7 : Semiring.{u3} S] [_inst_8 : SMul.{u3, u1} S R] [_inst_9 : Module.{u3, u2} S M _inst_7 _inst_2] [_inst_10 : IsScalarTower.{u3, u1, u2} S R M _inst_8 (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_3)))) (SMulZeroClass.toHasSmul.{u3, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u3, u2} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_7)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u3, u2} S M (Semiring.toMonoidWithZero.{u3} S _inst_7) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u3, u2} S M _inst_7 _inst_2 _inst_9))))], Eq.{succ u2} (Submodule.{u3, u2} S M _inst_7 _inst_2 _inst_9) (Submodule.span.{u3, u2} S M _inst_7 _inst_2 _inst_9 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p)) (Submodule.restrictScalars.{u3, u1, u2} S R M _inst_1 _inst_2 _inst_7 _inst_9 _inst_3 _inst_8 _inst_10 p)
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} {S : Type.{u3}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] (p : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) [_inst_7 : Semiring.{u3} S] [_inst_8 : SMul.{u3, u2} S R] [_inst_9 : Module.{u3, u1} S M _inst_7 _inst_2] [_inst_10 : IsScalarTower.{u3, u2, u1} S R M _inst_8 (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_3)))) (SMulZeroClass.toSMul.{u3, u1} S M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u1} S M (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_7)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S _inst_7) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u3, u1} S M _inst_7 _inst_2 _inst_9))))], Eq.{succ u1} (Submodule.{u3, u1} S M _inst_7 _inst_2 _inst_9) (Submodule.span.{u3, u1} S M _inst_7 _inst_2 _inst_9 (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) p)) (Submodule.restrictScalars.{u3, u2, u1} S R M _inst_1 _inst_2 _inst_7 _inst_9 _inst_3 _inst_8 _inst_10 p)
+  forall {R : Type.{u2}} {M : Type.{u1}} {S : Type.{u3}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] (p : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) [_inst_7 : Semiring.{u3} S] [_inst_8 : SMul.{u3, u2} S R] [_inst_9 : Module.{u3, u1} S M _inst_7 _inst_2] [_inst_10 : IsScalarTower.{u3, u2, u1} S R M _inst_8 (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_3)))) (SMulZeroClass.toSMul.{u3, u1} S M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u1} S M (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_7)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S _inst_7) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u3, u1} S M _inst_7 _inst_2 _inst_9))))], Eq.{succ u1} (Submodule.{u3, u1} S M _inst_7 _inst_2 _inst_9) (Submodule.span.{u3, u1} S M _inst_7 _inst_2 _inst_9 (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) p)) (Submodule.restrictScalars.{u3, u2, u1} S R M _inst_1 _inst_2 _inst_7 _inst_9 _inst_3 _inst_8 _inst_10 p)
 Case conversion may be inaccurate. Consider using '#align submodule.span_coe_eq_restrict_scalars Submodule.span_coe_eq_restrictScalarsₓ'. -/
 /-- A version of `submodule.span_eq` for when the span is by a smaller ring. -/
 @[simp]
@@ -179,7 +163,7 @@ alias Submodule.map_span ← _root_.linear_map.map_span
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u3} M) (N : Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)))) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) m s) -> (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M) (N : Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) m s) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) m) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.instSetLikeSubmodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M) (N : Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) m s) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) m) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 Case conversion may be inaccurate. Consider using '#align submodule.map_span_le Submodule.map_span_leₓ'. -/
 theorem map_span_le [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (s : Set M) (N : Submodule R₂ M₂) :
     map f (span R s) ≤ N ↔ ∀ m ∈ s, f m ∈ N :=
@@ -192,7 +176,7 @@ theorem map_span_le [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u3} M) (N : Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)))) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) m s) -> (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M) (N : Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) m s) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) m) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.instSetLikeSubmodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M) (N : Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) m s) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) m) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 Case conversion may be inaccurate. Consider using '#align linear_map.map_span_le LinearMap.map_span_leₓ'. -/
 alias Submodule.map_span_le ← _root_.linear_map.map_span_le
 #align linear_map.map_span_le LinearMap.map_span_le
@@ -238,7 +222,7 @@ alias Submodule.span_preimage_le ← _root_.linear_map.span_preimage_le
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) M (AddSubmonoid.setLike.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))) (AddSubmonoid.closure.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) s)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, HasSubset.Subset.{u2} (Set.{u2} M) (Set.instHasSubsetSet.{u2} M) (SetLike.coe.{u2, u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) M (AddSubmonoid.instSetLikeAddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (AddSubmonoid.closure.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) s)) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, HasSubset.Subset.{u2} (Set.{u2} M) (Set.instHasSubsetSet.{u2} M) (SetLike.coe.{u2, u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) M (AddSubmonoid.instSetLikeAddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (AddSubmonoid.closure.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) s)) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))
 Case conversion may be inaccurate. Consider using '#align submodule.closure_subset_span Submodule.closure_subset_spanₓ'. -/
 theorem closure_subset_span {s : Set M} : (AddSubmonoid.closure s : Set M) ⊆ span R s :=
   (@AddSubmonoid.closure_le _ _ _ (span R s).toAddSubmonoid).mpr subset_span
@@ -270,7 +254,7 @@ theorem span_closure {s : Set M} : span R (AddSubmonoid.closure s : Set M) = spa
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {s : Set.{u2} M} {p : M -> Prop}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (forall (x : M), (Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s) -> (p x)) -> (p (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))))))) -> (forall (x : M) (y : M), (p x) -> (p y) -> (p (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)))) x y))) -> (forall (a : R) (x : M), (p x) -> (p (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_3)))) a x))) -> (p x)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {s : Set.{u2} M} {p : M -> Prop}, (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (forall (x : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) -> (p x)) -> (p (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) -> (forall (x : M) (y : M), (p x) -> (p y) -> (p (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) x y))) -> (forall (a : R) (x : M), (p x) -> (p (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) a x))) -> (p x)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {s : Set.{u2} M} {p : M -> Prop}, (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (forall (x : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s) -> (p x)) -> (p (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) -> (forall (x : M) (y : M), (p x) -> (p y) -> (p (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) x y))) -> (forall (a : R) (x : M), (p x) -> (p (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) a x))) -> (p x)
 Case conversion may be inaccurate. Consider using '#align submodule.span_induction Submodule.span_inductionₓ'. -/
 /-- An induction principle for span membership. If `p` holds for 0 and all elements of `s`, and is
 preserved under addition and scalar multiplication, then `p` holds for all elements of the span of
@@ -285,7 +269,7 @@ theorem span_induction {p : M → Prop} (h : x ∈ span R s) (Hs : ∀ x ∈ s,
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M} {p : forall (x : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) -> Prop}, (forall (x : M) (h : Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s), p x (Submodule.subset_span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s x h)) -> (p (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)))))) (Submodule.zero_mem.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))) -> (forall (x : M) (hx : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (y : M) (hy : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)), (p x hx) -> (p y hy) -> (p (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)))) x y) (Submodule.add_mem.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) x y hx hy))) -> (forall (a : R) (x : M) (hx : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)), (p x hx) -> (p (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_3)))) a x) (Submodule.smul_mem.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) x a hx))) -> (forall {x : M} (hx : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)), p x hx)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M} {p : forall (x : M), (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) -> Prop}, (forall (x : M) (h : Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s), p x (Submodule.subset_span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s x h)) -> (p (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) (Submodule.zero_mem.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))) -> (forall (x : M) (hx : Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (y : M) (hy : Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)), (p x hx) -> (p y hy) -> (p (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) x y) (Submodule.add_mem.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) x y hx hy))) -> (forall (a : R) (x : M) (hx : Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)), (p x hx) -> (p (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) a x) (Submodule.smul_mem.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) x a hx))) -> (forall {x : M} (hx : Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)), p x hx)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M} {p : forall (x : M), (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) -> Prop}, (forall (x : M) (h : Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x s), p x (Submodule.subset_span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s x h)) -> (p (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) (Submodule.zero_mem.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))) -> (forall (x : M) (hx : Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (y : M) (hy : Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)), (p x hx) -> (p y hy) -> (p (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) x y) (Submodule.add_mem.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) x y hx hy))) -> (forall (a : R) (x : M) (hx : Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)), (p x hx) -> (p (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) a x) (Submodule.smul_mem.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) x a hx))) -> (forall {x : M} (hx : Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)), p x hx)
 Case conversion may be inaccurate. Consider using '#align submodule.span_induction' Submodule.span_induction'ₓ'. -/
 /-- A dependent version of `submodule.span_induction`. -/
 theorem span_induction' {p : ∀ x, x ∈ span R s → Prop} (Hs : ∀ (x) (h : x ∈ s), p x (subset_span h))
@@ -307,7 +291,7 @@ theorem span_induction' {p : ∀ x, x ∈ span R s → Prop} (Hs : ∀ (x) (h :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))) (Submodule.span.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Set.preimage.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) M ((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_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))))))) s)) (Top.top.{u2} (Submodule.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))) (Submodule.hasTop.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{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 _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))) (Submodule.span.{u1, u2} R (Subtype.{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 _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Set.preimage.{u2, u2} (Subtype.{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 _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)))) 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 _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)))) s)) (Top.top.{u2} (Submodule.{u1, u2} R (Subtype.{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 _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))) (Submodule.instTopSubmodule.{u1, u2} R (Subtype.{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 _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)))) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R (Subtype.{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 _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)))) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))) (Submodule.span.{u1, u2} R (Subtype.{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 _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)))) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Set.preimage.{u2, u2} (Subtype.{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 _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)))) 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 _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)))) s)) (Top.top.{u2} (Submodule.{u1, u2} R (Subtype.{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 _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)))) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))) (Submodule.instTopSubmodule.{u1, u2} R (Subtype.{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 _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)))) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))))
 Case conversion may be inaccurate. Consider using '#align submodule.span_span_coe_preimage Submodule.span_span_coe_preimageₓ'. -/
 @[simp]
 theorem span_span_coe_preimage : span R ((coe : span R s → M) ⁻¹' s) = ⊤ :=
@@ -376,7 +360,7 @@ variable (R M)
 lean 3 declaration is
   forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], GaloisInsertion.{u2, u2} (Set.{u2} M) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Set.{u2} M) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} M) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} M) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} M) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} M) (Set.completeBooleanAlgebra.{u2} M))))))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))))
 but is expected to have type
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], GaloisInsertion.{u2, u2} (Set.{u2} M) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Set.{u2} M) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} M) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} M) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} M) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} M) (Set.instCompleteBooleanAlgebraSet.{u2} M))))))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3))
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], GaloisInsertion.{u2, u2} (Set.{u2} M) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Set.{u2} M) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} M) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} M) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} M) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} M) (Set.instCompleteBooleanAlgebraSet.{u2} M))))))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))
 Case conversion may be inaccurate. Consider using '#align submodule.gi Submodule.giₓ'. -/
 /-- `span` forms a Galois insertion with the coercion from submodule to set. -/
 protected def gi : GaloisInsertion (@span R M _ _ _) coe
@@ -458,7 +442,7 @@ theorem span_attach_bunionᵢ [DecidableEq M] {α : Type _} (s : Finset α) (f :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Union.union.{u2} (Set.{u2} M) (Set.hasUnion.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p) 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Union.union.{u2} (Set.{u2} M) (Set.instUnionSet.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) s))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Union.union.{u2} (Set.{u2} M) (Set.instUnionSet.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) s))
 Case conversion may be inaccurate. Consider using '#align submodule.sup_span Submodule.sup_spanₓ'. -/
 theorem sup_span : p ⊔ span R s = span R (p ∪ s) := by rw [Submodule.span_union, p.span_eq]
 #align submodule.sup_span Submodule.sup_span
@@ -467,7 +451,7 @@ theorem sup_span : p ⊔ span R s = span R (p ∪ s) := by rw [Submodule.span_un
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) p) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Union.union.{u2} (Set.{u2} M) (Set.hasUnion.{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 _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) p) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Union.union.{u2} (Set.{u2} M) (Set.instUnionSet.{u2} M) s (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) p) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Union.union.{u2} (Set.{u2} M) (Set.instUnionSet.{u2} M) s (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) p)))
 Case conversion may be inaccurate. Consider using '#align submodule.span_sup Submodule.span_supₓ'. -/
 theorem span_sup : span R s ⊔ p = span R (s ∪ p) := by rw [Submodule.span_union, p.span_eq]
 #align submodule.span_sup Submodule.span_sup
@@ -511,16 +495,12 @@ theorem span_smul_le (s : Set M) (r : R) : span R (r • s) ≤ span R s :=
   exact smul_mem (span R s) r (subset_span hx)
 #align submodule.span_smul_le Submodule.span_smul_le
 
-/- warning: submodule.subset_span_trans -> Submodule.subset_span_trans 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {U : Set.{u2} M} {V : Set.{u2} M} {W : Set.{u2} M}, (HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) U ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 V))) -> (HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) V ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 W))) -> (HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) U ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 W)))
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {U : Set.{u2} M} {V : Set.{u2} M} {W : Set.{u2} M}, (HasSubset.Subset.{u2} (Set.{u2} M) (Set.instHasSubsetSet.{u2} M) U (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 V))) -> (HasSubset.Subset.{u2} (Set.{u2} M) (Set.instHasSubsetSet.{u2} M) V (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 W))) -> (HasSubset.Subset.{u2} (Set.{u2} M) (Set.instHasSubsetSet.{u2} M) U (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 W)))
-Case conversion may be inaccurate. Consider using '#align submodule.subset_span_trans Submodule.subset_span_transₓ'. -/
+#print Submodule.subset_span_trans /-
 theorem subset_span_trans {U V W : Set M} (hUV : U ⊆ Submodule.span R V)
     (hVW : V ⊆ Submodule.span R W) : U ⊆ Submodule.span R W :=
   (Submodule.gi R M).gc.le_u_l_trans hUV hVW
 #align submodule.subset_span_trans Submodule.subset_span_trans
+-/
 
 #print Submodule.span_smul_eq_of_isUnit /-
 /-- See `submodule.span_smul_eq` (in `ring_theory.ideal.operations`) for
@@ -540,7 +520,7 @@ theorem span_smul_eq_of_isUnit (s : Set M) (r : R) (hr : IsUnit r) : span R (r 
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} [hι : Nonempty.{u3} ι] (S : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Directed.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) S) -> (Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u2, u3} M ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (S i))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} [hι : Nonempty.{u3} ι] (S : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), (Directed.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.5760 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.5762 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.5760 x._@.Mathlib.LinearAlgebra.Span._hyg.5762) S) -> (Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u1, u3} M ι (fun (i : ι) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (S i))))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} [hι : Nonempty.{u3} ι] (S : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), (Directed.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.5760 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.5762 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.5760 x._@.Mathlib.LinearAlgebra.Span._hyg.5762) S) -> (Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u1, u3} M ι (fun (i : ι) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (S i))))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_supr_of_directed Submodule.coe_supᵢ_of_directedₓ'. -/
 @[simp]
 theorem coe_supᵢ_of_directed {ι} [hι : Nonempty ι] (S : ι → Submodule R M)
@@ -561,7 +541,7 @@ theorem coe_supᵢ_of_directed {ι} [hι : Nonempty ι] (S : ι → Submodule R
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} [_inst_7 : Nonempty.{u3} ι] (S : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Directed.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) S) -> (forall {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι S)) (Exists.{u3} ι (fun (i : ι) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (S i))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} [_inst_7 : Nonempty.{u3} ι] (S : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), (Directed.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.6058 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.6060 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.6058 x._@.Mathlib.LinearAlgebra.Span._hyg.6060) S) -> (forall {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι S)) (Exists.{u3} ι (fun (i : ι) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (S i))))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} [_inst_7 : Nonempty.{u3} ι] (S : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), (Directed.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.6058 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.6060 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.6058 x._@.Mathlib.LinearAlgebra.Span._hyg.6060) S) -> (forall {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι S)) (Exists.{u3} ι (fun (i : ι) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (S i))))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_of_directed Submodule.mem_supᵢ_of_directedₓ'. -/
 @[simp]
 theorem mem_supᵢ_of_directed {ι} [Nonempty ι] (S : ι → Submodule R M) (H : Directed (· ≤ ·) S) {x} :
@@ -575,7 +555,7 @@ theorem mem_supᵢ_of_directed {ι} [Nonempty ι] (S : ι → Submodule R M) (H
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {z : M}, (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) s) -> (DirectedOn.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) s) -> (Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (SupSet.supₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) s)) (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (y : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Exists.{0} (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) (fun (H : Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z y))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {z : M}, (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) s) -> (DirectedOn.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.6191 : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.6193 : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.6191 x._@.Mathlib.LinearAlgebra.Span._hyg.6193) s) -> (Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (SupSet.supₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) s)) (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (y : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => And (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z y))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {z : M}, (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) s) -> (DirectedOn.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.6191 : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.6193 : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.6191 x._@.Mathlib.LinearAlgebra.Span._hyg.6193) s) -> (Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (SupSet.supₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) s)) (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (y : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => And (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z y))))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_Sup_of_directed Submodule.mem_supₛ_of_directedₓ'. -/
 theorem mem_supₛ_of_directed {s : Set (Submodule R M)} {z} (hs : s.Nonempty)
     (hdir : DirectedOn (· ≤ ·) s) : z ∈ supₛ s ↔ ∃ y ∈ s, z ∈ y :=
@@ -588,7 +568,7 @@ theorem mem_supₛ_of_directed {s : Set (Submodule R M)} {z} (hs : s.Nonempty)
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (a : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))), Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (supᵢ.{u2, 1} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) Nat (fun (k : Nat) => coeFn.{succ u2, succ u2} (OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (fun (_x : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) => Nat -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (OrderHom.hasCoeToFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k))) (Set.unionᵢ.{u2, 1} M Nat (fun (k : Nat) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (coeFn.{succ u2, succ u2} (OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (fun (_x : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) => Nat -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (OrderHom.hasCoeToFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (a : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (supᵢ.{u2, 1} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) Nat (fun (k : Nat) => OrderHom.toFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k))) (Set.unionᵢ.{u2, 1} M Nat (fun (k : Nat) => SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OrderHom.toFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (a : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (supᵢ.{u2, 1} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) Nat (fun (k : Nat) => OrderHom.toFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k))) (Set.unionᵢ.{u2, 1} M Nat (fun (k : Nat) => SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OrderHom.toFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k)))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_supr_of_chain Submodule.coe_supᵢ_of_chainₓ'. -/
 @[norm_cast, simp]
 theorem coe_supᵢ_of_chain (a : ℕ →o Submodule R M) : (↑(⨆ k, a k) : Set M) = ⋃ k, (a k : Set M) :=
@@ -599,7 +579,7 @@ theorem coe_supᵢ_of_chain (a : ℕ →o Submodule R M) : (↑(⨆ k, a k) : Se
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], OmegaCompletePartialOrder.Continuous'.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CompleteLattice.omegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (CompleteLattice.omegaCompletePartialOrder.{u2} (Set.{u2} M) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} M) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} M) (Set.completeBooleanAlgebra.{u2} M))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], OmegaCompletePartialOrder.Continuous'.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} M) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} M) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} M) (Set.instCompleteBooleanAlgebraSet.{u2} M))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], OmegaCompletePartialOrder.Continuous'.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} M) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} M) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} M) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} M) (Set.instCompleteBooleanAlgebraSet.{u2} M))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_scott_continuous Submodule.coe_scott_continuousₓ'. -/
 /-- We can regard `coe_supr_of_chain` as the statement that `coe : (submodule R M) → set M` is
 Scott continuous for the ω-complete partial order induced by the complete lattice structures. -/
@@ -612,7 +592,7 @@ theorem coe_scott_continuous :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (a : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (m : M), Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u2, 1} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) Nat (fun (k : Nat) => coeFn.{succ u2, succ u2} (OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (fun (_x : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) => Nat -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (OrderHom.hasCoeToFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k))) (Exists.{1} Nat (fun (k : Nat) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (coeFn.{succ u2, succ u2} (OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (fun (_x : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) => Nat -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (OrderHom.hasCoeToFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (a : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (m : M), Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u2, 1} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) Nat (fun (k : Nat) => OrderHom.toFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k))) (Exists.{1} Nat (fun (k : Nat) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (OrderHom.toFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (a : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (m : M), Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u2, 1} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) Nat (fun (k : Nat) => OrderHom.toFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k))) (Exists.{1} Nat (fun (k : Nat) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (OrderHom.toFun.{0, u2} Nat (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) a k)))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_of_chain Submodule.mem_supᵢ_of_chainₓ'. -/
 @[simp]
 theorem mem_supᵢ_of_chain (a : ℕ →o Submodule R M) (m : M) : (m ∈ ⨆ k, a k) ↔ ∃ k, m ∈ a k :=
@@ -627,7 +607,7 @@ variable {p p'}
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (Exists.{succ u2} M (fun (y : M) => Exists.{0} (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y p) (fun (H : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y p) => Exists.{succ u2} M (fun (z : M) => Exists.{0} (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z p') (fun (H : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z p') => 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)))) y z) x)))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (Exists.{succ u2} M (fun (y : M) => And (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y p) (Exists.{succ u2} M (fun (z : M) => And (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z p') (Eq.{succ u2} M (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) y z) x)))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (Exists.{succ u2} M (fun (y : M) => And (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y p) (Exists.{succ u2} M (fun (z : M) => And (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z p') (Eq.{succ u2} M (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) y z) x)))))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_sup Submodule.mem_supₓ'. -/
 theorem mem_sup : x ∈ p ⊔ p' ↔ ∃ y ∈ p, ∃ z ∈ p', y + z = x :=
   ⟨fun h => by
@@ -649,7 +629,7 @@ theorem mem_sup : x ∈ p ⊔ p' ↔ ∃ y ∈ p, ∃ z ∈ p', y + z = x :=
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (Exists.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) (fun (y : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) => Exists.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p') (fun (z : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p') => 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)))) ((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_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p))))) y) ((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_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p') M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p') M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p') M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p') M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p'))))) z)) x)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (Exists.{succ u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p)) (fun (y : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p)) => Exists.{succ u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p')) (fun (z : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p')) => Eq.{succ u2} M (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) (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 _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p)) y) (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 _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p')) z)) x)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (Exists.{succ u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p)) (fun (y : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p)) => Exists.{succ u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p')) (fun (z : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p')) => Eq.{succ u2} M (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) (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 _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) p)) y) (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 _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) p')) z)) x)))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_sup' Submodule.mem_sup'ₓ'. -/
 theorem mem_sup' : x ∈ p ⊔ p' ↔ ∃ (y : p)(z : p'), (y : M) + z = x :=
   mem_sup.trans <| by simp only [SetLike.exists, coe_mk]
@@ -661,7 +641,7 @@ variable (p p')
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (HAdd.hAdd.{u2, u2, u2} (Set.{u2} M) (Set.{u2} M) (Set.{u2} M) (instHAdd.{u2} (Set.{u2} M) (Set.add.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p'))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (HAdd.hAdd.{u2, u2, u2} (Set.{u2} M) (Set.{u2} M) (Set.{u2} M) (instHAdd.{u2} (Set.{u2} M) (Set.add.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p'))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (HAdd.hAdd.{u2, u2, u2} (Set.{u2} M) (Set.{u2} M) (Set.{u2} M) (instHAdd.{u2} (Set.{u2} M) (Set.add.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) p'))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_sup Submodule.coe_supₓ'. -/
 theorem coe_sup : ↑(p ⊔ p') = (p + p' : Set M) :=
   by
@@ -699,21 +679,17 @@ theorem sup_toAddSubgroup {R M : Type _} [Ring R] [AddCommGroup M] [Module R M]
 
 end
 
-/- warning: submodule.mem_span_singleton_self -> Submodule.mem_span_singleton_self is a dubious translation:
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-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (x : M), Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_span_singleton_self Submodule.mem_span_singleton_selfₓ'. -/
+#print Submodule.mem_span_singleton_self /-
 theorem mem_span_singleton_self (x : M) : x ∈ R ∙ x :=
   subset_span rfl
 #align submodule.mem_span_singleton_self Submodule.mem_span_singleton_self
+-/
 
 /- warning: submodule.nontrivial_span_singleton -> Submodule.nontrivial_span_singleton 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M}, (Ne.{succ u2} M x (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))))))) -> (Nontrivial.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M}, (Ne.{succ u2} M x (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) -> (Nontrivial.{u2} (Subtype.{succ u2} M (fun (x_1 : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x_1 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M}, (Ne.{succ u2} M x (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) -> (Nontrivial.{u2} (Subtype.{succ u2} M (fun (x_1 : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x_1 (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)))))
 Case conversion may be inaccurate. Consider using '#align submodule.nontrivial_span_singleton Submodule.nontrivial_span_singletonₓ'. -/
 theorem nontrivial_span_singleton {x : M} (h : x ≠ 0) : Nontrivial (R ∙ x) :=
   ⟨by
@@ -723,12 +699,7 @@ theorem nontrivial_span_singleton {x : M} (h : x ≠ 0) : Nontrivial (R ∙ x) :
     exact h H⟩
 #align submodule.nontrivial_span_singleton Submodule.nontrivial_span_singleton
 
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-Case conversion may be inaccurate. Consider using '#align submodule.mem_span_singleton Submodule.mem_span_singletonₓ'. -/
+#print Submodule.mem_span_singleton /-
 theorem mem_span_singleton {y : M} : (x ∈ R ∙ y) ↔ ∃ a : R, a • y = x :=
   ⟨fun h => by
     apply span_induction h
@@ -741,12 +712,13 @@ theorem mem_span_singleton {y : M} : (x ∈ R ∙ y) ↔ ∃ a : R, a • y = x
       exact ⟨a * b, by simp [smul_smul]⟩, by
     rintro ⟨a, y, rfl⟩ <;> exact smul_mem _ _ (subset_span <| by simp)⟩
 #align submodule.mem_span_singleton Submodule.mem_span_singleton
+-/
 
 /- warning: submodule.le_span_singleton_iff -> Submodule.le_span_singleton_iff 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {v₀ : M}, Iff (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) s (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) v₀))) (forall (v : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) v s) -> (Exists.{succ u1} R (fun (r : R) => Eq.{succ u2} M (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_3)))) r v₀) v)))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3} {v₀ : M}, Iff (LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) s (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) v₀))) (forall (v : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) v s) -> (Exists.{succ u2} R (fun (r : R) => Eq.{succ u1} M (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_3))))) r v₀) v)))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3} {v₀ : M}, Iff (LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) s (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) v₀))) (forall (v : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) v s) -> (Exists.{succ u2} R (fun (r : R) => Eq.{succ u1} M (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_3))))) r v₀) v)))
 Case conversion may be inaccurate. Consider using '#align submodule.le_span_singleton_iff Submodule.le_span_singleton_iffₓ'. -/
 theorem le_span_singleton_iff {s : Submodule R M} {v₀ : M} :
     (s ≤ R ∙ v₀) ↔ ∀ v ∈ s, ∃ r : R, r • v₀ = v := by simp_rw [SetLike.le_def, mem_span_singleton]
@@ -779,15 +751,11 @@ theorem span_zero_singleton : (R ∙ (0 : M)) = ⊥ :=
   simp [mem_span_singleton, eq_comm]
 #align submodule.span_zero_singleton Submodule.span_zero_singleton
 
-/- warning: submodule.span_singleton_eq_range -> Submodule.span_singleton_eq_range 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (y : M), Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) y))) (Set.range.{u2, succ u1} M R (fun (_x : R) => 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_3)))) _x y))
-but is expected to have type
-  forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (y : M), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) y))) (Set.range.{u2, succ u1} M R (fun (_x : R) => HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) _x y))
-Case conversion may be inaccurate. Consider using '#align submodule.span_singleton_eq_range Submodule.span_singleton_eq_rangeₓ'. -/
+#print Submodule.span_singleton_eq_range /-
 theorem span_singleton_eq_range (y : M) : ↑(R ∙ y) = range ((· • y) : R → M) :=
   Set.ext fun x => mem_span_singleton
 #align submodule.span_singleton_eq_range Submodule.span_singleton_eq_range
+-/
 
 /- warning: submodule.span_singleton_smul_le -> Submodule.span_singleton_smul_le is a dubious translation:
 lean 3 declaration is
@@ -835,7 +803,7 @@ theorem span_singleton_smul_eq {r : R} (hr : IsUnit r) (x : M) : (R ∙ r • x)
 lean 3 declaration is
   forall {K : Type.{u1}} {E : Type.{u2}} [_inst_7 : DivisionRing.{u1} K] [_inst_8 : AddCommGroup.{u2} E] [_inst_9 : Module.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8)] {s : Submodule.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8) _inst_9} {x : E}, Iff (Disjoint.{u2} (Submodule.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8) _inst_9) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8) _inst_9) E (Submodule.setLike.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8) _inst_9)) (Submodule.orderBot.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8) _inst_9) s (Submodule.span.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8) _inst_9 (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) x))) ((Membership.Mem.{u2, u2} E (Submodule.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8) _inst_9) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8) _inst_9) E (Submodule.setLike.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8) _inst_9)) x s) -> (Eq.{succ u2} E x (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_8))))))))))
 but is expected to have type
-  forall {K : Type.{u2}} {E : Type.{u1}} [_inst_7 : DivisionRing.{u2} K] [_inst_8 : AddCommGroup.{u1} E] [_inst_9 : Module.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8)] {s : Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9} {x : E}, Iff (Disjoint.{u1} (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) (Submodule.completeLattice.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) s (Submodule.span.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9 (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) x))) ((Membership.mem.{u1, u1} E (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) E (Submodule.instSetLikeSubmodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9)) x s) -> (Eq.{succ u1} E x (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_8)))))))))
+  forall {K : Type.{u2}} {E : Type.{u1}} [_inst_7 : DivisionRing.{u2} K] [_inst_8 : AddCommGroup.{u1} E] [_inst_9 : Module.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8)] {s : Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9} {x : E}, Iff (Disjoint.{u1} (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) (Submodule.completeLattice.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) s (Submodule.span.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9 (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) x))) ((Membership.mem.{u1, u1} E (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) E (Submodule.setLike.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9)) x s) -> (Eq.{succ u1} E x (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_8)))))))))
 Case conversion may be inaccurate. Consider using '#align submodule.disjoint_span_singleton Submodule.disjoint_span_singletonₓ'. -/
 theorem disjoint_span_singleton {K E : Type _} [DivisionRing K] [AddCommGroup E] [Module K E]
     {s : Submodule K E} {x : E} : Disjoint s (K ∙ x) ↔ x ∈ s → x = 0 :=
@@ -853,30 +821,26 @@ theorem disjoint_span_singleton {K E : Type _} [DivisionRing K] [AddCommGroup E]
 lean 3 declaration is
   forall {K : Type.{u1}} {E : Type.{u2}} [_inst_7 : DivisionRing.{u1} K] [_inst_8 : AddCommGroup.{u2} E] [_inst_9 : Module.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8)] {p : Submodule.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8) _inst_9} {x : E}, (Ne.{succ u2} E x (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_8))))))))) -> (Iff (Disjoint.{u2} (Submodule.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8) _inst_9) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8) _inst_9) E (Submodule.setLike.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8) _inst_9)) (Submodule.orderBot.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8) _inst_9) p (Submodule.span.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8) _inst_9 (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) x))) (Not (Membership.Mem.{u2, u2} E (Submodule.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8) _inst_9) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8) _inst_9) E (Submodule.setLike.{u1, u2} K E (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_8) _inst_9)) x p)))
 but is expected to have type
-  forall {K : Type.{u2}} {E : Type.{u1}} [_inst_7 : DivisionRing.{u2} K] [_inst_8 : AddCommGroup.{u1} E] [_inst_9 : Module.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8)] {p : Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9} {x : E}, (Ne.{succ u1} E x (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_8)))))))) -> (Iff (Disjoint.{u1} (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) (Submodule.completeLattice.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderInstSetLikeSubmodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) p (Submodule.span.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9 (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) x))) (Not (Membership.mem.{u1, u1} E (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) E (Submodule.instSetLikeSubmodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9)) x p)))
+  forall {K : Type.{u2}} {E : Type.{u1}} [_inst_7 : DivisionRing.{u2} K] [_inst_8 : AddCommGroup.{u1} E] [_inst_9 : Module.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8)] {p : Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9} {x : E}, (Ne.{succ u1} E x (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_8)))))))) -> (Iff (Disjoint.{u1} (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) (Submodule.completeLattice.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) p (Submodule.span.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9 (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) x))) (Not (Membership.mem.{u1, u1} E (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9) E (Submodule.setLike.{u2, u1} K E (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_7)) (AddCommGroup.toAddCommMonoid.{u1} E _inst_8) _inst_9)) x p)))
 Case conversion may be inaccurate. Consider using '#align submodule.disjoint_span_singleton' Submodule.disjoint_span_singleton'ₓ'. -/
 theorem disjoint_span_singleton' {K E : Type _} [DivisionRing K] [AddCommGroup E] [Module K E]
     {p : Submodule K E} {x : E} (x0 : x ≠ 0) : Disjoint p (K ∙ x) ↔ x ∉ p :=
   disjoint_span_singleton.trans ⟨fun h₁ h₂ => x0 (h₁ h₂), fun h₁ h₂ => (h₁ h₂).elim⟩
 #align submodule.disjoint_span_singleton' Submodule.disjoint_span_singleton'
 
-/- warning: submodule.mem_span_singleton_trans -> Submodule.mem_span_singleton_trans 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {y : M} {z : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) y))) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) z))) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) z)))
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {y : M} {z : M}, (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) y))) -> (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) z))) -> (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) z)))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_span_singleton_trans Submodule.mem_span_singleton_transₓ'. -/
+#print Submodule.mem_span_singleton_trans /-
 theorem mem_span_singleton_trans {x y z : M} (hxy : x ∈ R ∙ y) (hyz : y ∈ R ∙ z) : x ∈ R ∙ z :=
   by
   rw [← SetLike.mem_coe, ← singleton_subset_iff] at *
   exact Submodule.subset_span_trans hxy hyz
 #align submodule.mem_span_singleton_trans Submodule.mem_span_singleton_trans
+-/
 
 /- warning: submodule.mem_span_insert -> Submodule.mem_span_insert 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {s : Set.{u2} M} {y : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Insert.insert.{u2, u2} M (Set.{u2} M) (Set.hasInsert.{u2} M) y s))) (Exists.{succ u1} R (fun (a : R) => Exists.{succ u2} M (fun (z : M) => Exists.{0} (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (fun (H : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) => Eq.{succ u2} M x (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_3)))) a y) z)))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {s : Set.{u2} M} {y : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Insert.insert.{u2, u2} M (Set.{u2} M) (Set.instInsertSet.{u2} M) y s))) (Exists.{succ u1} R (fun (a : R) => Exists.{succ u2} M (fun (z : M) => And (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Eq.{succ u2} M x (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) a y) z)))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {s : Set.{u2} M} {y : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Insert.insert.{u2, u2} M (Set.{u2} M) (Set.instInsertSet.{u2} M) y s))) (Exists.{succ u1} R (fun (a : R) => Exists.{succ u2} M (fun (z : M) => And (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Eq.{succ u2} M x (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) a y) z)))))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_span_insert Submodule.mem_span_insertₓ'. -/
 theorem mem_span_insert {y} : x ∈ span R (insert y s) ↔ ∃ a : R, ∃ z ∈ span R s, x = a • y + z :=
   by
@@ -890,7 +854,7 @@ theorem mem_span_insert {y} : x ∈ span R (insert y s) ↔ ∃ a : R, ∃ z ∈
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {y : M} {z : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Insert.insert.{u2, u2} M (Set.{u2} M) (Set.hasInsert.{u2} M) x (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) y)))) (Exists.{succ u1} R (fun (a : R) => Exists.{succ u1} R (fun (b : R) => 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_3)))) a x) (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_3)))) b y)) z)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {y : M} {z : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Insert.insert.{u2, u2} M (Set.{u2} M) (Set.instInsertSet.{u2} M) x (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) y)))) (Exists.{succ u1} R (fun (a : R) => Exists.{succ u1} R (fun (b : R) => Eq.{succ u2} M (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) a x) (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) b y)) z)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {y : M} {z : M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Insert.insert.{u2, u2} M (Set.{u2} M) (Set.instInsertSet.{u2} M) x (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) y)))) (Exists.{succ u1} R (fun (a : R) => Exists.{succ u1} R (fun (b : R) => Eq.{succ u2} M (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) a x) (HSMul.hSMul.{u1, u2, u2} R M M (instHSMul.{u1, u2} R M (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) b y)) z)))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_span_pair Submodule.mem_span_pairₓ'. -/
 theorem mem_span_pair {x y z : M} : z ∈ span R ({x, y} : Set M) ↔ ∃ a b : R, a • x + b • y = z := by
   simp_rw [mem_span_insert, mem_span_singleton, exists_prop, exists_exists_eq_and, eq_comm]
@@ -906,25 +870,17 @@ theorem span_insert (x) (s : Set M) : span R (insert x s) = span R ({x} : Set M)
   rw [insert_eq, span_union]
 #align submodule.span_insert Submodule.span_insert
 
-/- warning: submodule.span_insert_eq_span -> Submodule.span_insert_eq_span 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {s : Set.{u2} M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Insert.insert.{u2, u2} M (Set.{u2} M) (Set.hasInsert.{u2} M) x s)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {s : Set.{u2} M}, (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Insert.insert.{u2, u2} M (Set.{u2} M) (Set.instInsertSet.{u2} M) x s)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))
-Case conversion may be inaccurate. Consider using '#align submodule.span_insert_eq_span Submodule.span_insert_eq_spanₓ'. -/
+#print Submodule.span_insert_eq_span /-
 theorem span_insert_eq_span (h : x ∈ span R s) : span R (insert x s) = span R s :=
   span_eq_of_le _ (Set.insert_subset.mpr ⟨h, subset_span⟩) (span_mono <| subset_insert _ _)
 #align submodule.span_insert_eq_span Submodule.span_insert_eq_span
+-/
 
-/- warning: submodule.span_span -> Submodule.span_span 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)
-Case conversion may be inaccurate. Consider using '#align submodule.span_span Submodule.span_spanₓ'. -/
+#print Submodule.span_span /-
 theorem span_span : span R (span R s : Set M) = span R s :=
   span_eq _
 #align submodule.span_span Submodule.span_span
+-/
 
 variable (R S s)
 
@@ -944,7 +900,7 @@ theorem span_le_restrictScalars [Semiring S] [SMul R S] [Module S M] [IsScalarTo
 lean 3 declaration is
   forall (R : Type.{u1}) {M : Type.{u2}} (S : Type.{u3}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (s : Set.{u2} M) [_inst_7 : Semiring.{u3} S] [_inst_8 : SMul.{u1, u3} R S] [_inst_9 : Module.{u3, u2} S M _inst_7 _inst_2] [_inst_10 : IsScalarTower.{u1, u3, u2} R S M _inst_8 (SMulZeroClass.toHasSmul.{u3, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u3, u2} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_7)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u3, u2} S M (Semiring.toMonoidWithZero.{u3} S _inst_7) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u3, u2} S M _inst_7 _inst_2 _inst_9)))) (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_3))))], HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u3, u2} S M _inst_7 _inst_2 _inst_9) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u3, u2} S M _inst_7 _inst_2 _inst_9) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u3, u2} S M _inst_7 _inst_2 _inst_9) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u3, u2} S M _inst_7 _inst_2 _inst_9) M (Submodule.setLike.{u3, u2} S M _inst_7 _inst_2 _inst_9)))) (Submodule.span.{u3, u2} S M _inst_7 _inst_2 _inst_9 s))
 but is expected to have type
-  forall (R : Type.{u2}) {M : Type.{u1}} (S : Type.{u3}) [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] (s : Set.{u1} M) [_inst_7 : Semiring.{u3} S] [_inst_8 : SMul.{u2, u3} R S] [_inst_9 : Module.{u3, u1} S M _inst_7 _inst_2] [_inst_10 : IsScalarTower.{u2, u3, u1} R S M _inst_8 (SMulZeroClass.toSMul.{u3, u1} S M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u1} S M (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_7)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S _inst_7) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u3, u1} S M _inst_7 _inst_2 _inst_9)))) (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_3))))], HasSubset.Subset.{u1} (Set.{u1} M) (Set.instHasSubsetSet.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 s)) (SetLike.coe.{u1, u1} (Submodule.{u3, u1} S M _inst_7 _inst_2 _inst_9) M (Submodule.instSetLikeSubmodule.{u3, u1} S M _inst_7 _inst_2 _inst_9) (Submodule.span.{u3, u1} S M _inst_7 _inst_2 _inst_9 s))
+  forall (R : Type.{u2}) {M : Type.{u1}} (S : Type.{u3}) [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] (s : Set.{u1} M) [_inst_7 : Semiring.{u3} S] [_inst_8 : SMul.{u2, u3} R S] [_inst_9 : Module.{u3, u1} S M _inst_7 _inst_2] [_inst_10 : IsScalarTower.{u2, u3, u1} R S M _inst_8 (SMulZeroClass.toSMul.{u3, u1} S M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u1} S M (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_7)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S _inst_7) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u3, u1} S M _inst_7 _inst_2 _inst_9)))) (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_3))))], HasSubset.Subset.{u1} (Set.{u1} M) (Set.instHasSubsetSet.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 s)) (SetLike.coe.{u1, u1} (Submodule.{u3, u1} S M _inst_7 _inst_2 _inst_9) M (Submodule.setLike.{u3, u1} S M _inst_7 _inst_2 _inst_9) (Submodule.span.{u3, u1} S M _inst_7 _inst_2 _inst_9 s))
 Case conversion may be inaccurate. Consider using '#align submodule.span_subset_span Submodule.span_subset_spanₓ'. -/
 /-- A version of `submodule.span_le_restrict_scalars` with coercions. -/
 @[simp]
@@ -957,7 +913,7 @@ theorem span_subset_span [Semiring S] [SMul R S] [Module S M] [IsScalarTower R S
 lean 3 declaration is
   forall (R : Type.{u1}) {M : Type.{u2}} (S : Type.{u3}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (s : Set.{u2} M) [_inst_7 : Semiring.{u3} S] [_inst_8 : SMul.{u1, u3} R S] [_inst_9 : Module.{u3, u2} S M _inst_7 _inst_2] [_inst_10 : IsScalarTower.{u1, u3, u2} R S M _inst_8 (SMulZeroClass.toHasSmul.{u3, u2} S M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u3, u2} S M (MulZeroClass.toHasZero.{u3} S (MulZeroOneClass.toMulZeroClass.{u3} S (MonoidWithZero.toMulZeroOneClass.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_7)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u3, u2} S M (Semiring.toMonoidWithZero.{u3} S _inst_7) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u3, u2} S M _inst_7 _inst_2 _inst_9)))) (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_3))))], Eq.{succ u2} (Submodule.{u3, u2} S M _inst_7 _inst_2 _inst_9) (Submodule.span.{u3, u2} S M _inst_7 _inst_2 _inst_9 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))) (Submodule.span.{u3, u2} S M _inst_7 _inst_2 _inst_9 s)
 but is expected to have type
-  forall (R : Type.{u2}) {M : Type.{u1}} (S : Type.{u3}) [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] (s : Set.{u1} M) [_inst_7 : Semiring.{u3} S] [_inst_8 : SMul.{u2, u3} R S] [_inst_9 : Module.{u3, u1} S M _inst_7 _inst_2] [_inst_10 : IsScalarTower.{u2, u3, u1} R S M _inst_8 (SMulZeroClass.toSMul.{u3, u1} S M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u1} S M (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_7)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S _inst_7) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u3, u1} S M _inst_7 _inst_2 _inst_9)))) (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_3))))], Eq.{succ u1} (Submodule.{u3, u1} S M _inst_7 _inst_2 _inst_9) (Submodule.span.{u3, u1} S M _inst_7 _inst_2 _inst_9 (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 s))) (Submodule.span.{u3, u1} S M _inst_7 _inst_2 _inst_9 s)
+  forall (R : Type.{u2}) {M : Type.{u1}} (S : Type.{u3}) [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] (s : Set.{u1} M) [_inst_7 : Semiring.{u3} S] [_inst_8 : SMul.{u2, u3} R S] [_inst_9 : Module.{u3, u1} S M _inst_7 _inst_2] [_inst_10 : IsScalarTower.{u2, u3, u1} R S M _inst_8 (SMulZeroClass.toSMul.{u3, u1} S M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u3, u1} S M (MonoidWithZero.toZero.{u3} S (Semiring.toMonoidWithZero.{u3} S _inst_7)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u3, u1} S M (Semiring.toMonoidWithZero.{u3} S _inst_7) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u3, u1} S M _inst_7 _inst_2 _inst_9)))) (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_3))))], Eq.{succ u1} (Submodule.{u3, u1} S M _inst_7 _inst_2 _inst_9) (Submodule.span.{u3, u1} S M _inst_7 _inst_2 _inst_9 (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 s))) (Submodule.span.{u3, u1} S M _inst_7 _inst_2 _inst_9 s)
 Case conversion may be inaccurate. Consider using '#align submodule.span_span_of_tower Submodule.span_span_of_towerₓ'. -/
 /-- Taking the span by a large ring of the span by the small ring is the same as taking the span
 by just the large ring. -/
@@ -1057,7 +1013,7 @@ theorem span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂)
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u3} M}, (Membership.Mem.{u3, u3} M (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) -> (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u2} M}, (Membership.mem.{u2, u2} M (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u4, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.instSetLikeSubmodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u2} M}, (Membership.mem.{u2, u2} M (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u4, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))
 Case conversion may be inaccurate. Consider using '#align submodule.apply_mem_span_image_of_mem_span Submodule.apply_mem_span_image_of_mem_spanₓ'. -/
 theorem apply_mem_span_image_of_mem_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) {x : M}
     {s : Set M} (h : x ∈ Submodule.span R s) : f x ∈ Submodule.span R₂ (f '' s) :=
@@ -1070,7 +1026,7 @@ theorem apply_mem_span_image_of_mem_span [RingHomSurjective σ₁₂] (f : M →
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} (x : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.map.{u1, u1, u2, u2, u2} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_2 (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_2 (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_2 (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Submodule.subtype.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.span.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Singleton.singleton.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) (Set.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p)) (Set.hasSingleton.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p)) x))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) ((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_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p))))) x)))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {p : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3} (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)), Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.map.{u2, u2, u1, u1, u1} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) M _inst_1 _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomSurjective.ids.{u2} R _inst_1) (LinearMap.{u2, u2, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) M (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) M _inst_1 _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_2 (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Submodule.subtype.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.span.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) _inst_1 (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Singleton.singleton.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) (Set.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p))) (Set.instSingletonSet.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p))) x))) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) (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_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) p)) x)))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {p : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3} (x : Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)), Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.map.{u2, u2, u1, u1, u1} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) M _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_2 (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomSurjective.ids.{u2} R _inst_1) (LinearMap.{u2, u2, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) M (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_2 (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) M _inst_1 _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_2 (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Submodule.subtype.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.span.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 p) (Singleton.singleton.{u1, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p)) (Set.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p))) (Set.instSingletonSet.{u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x p))) x))) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) (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_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) p)) x)))
 Case conversion may be inaccurate. Consider using '#align submodule.map_subtype_span_singleton Submodule.map_subtype_span_singletonₓ'. -/
 @[simp]
 theorem map_subtype_span_singleton {p : Submodule R M} (x : p) :
@@ -1081,7 +1037,7 @@ theorem map_subtype_span_singleton {p : Submodule R M} (x : p) :
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u3} M}, (Not (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))) -> (Not (Membership.Mem.{u3, u3} M (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u2} M}, (Not (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.instSetLikeSubmodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))) -> (Not (Membership.mem.{u2, u2} M (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u4, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u2} M}, (Not (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))) -> (Not (Membership.mem.{u2, u2} M (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u4, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)))
 Case conversion may be inaccurate. Consider using '#align submodule.not_mem_span_of_apply_not_mem_span_image Submodule.not_mem_span_of_apply_not_mem_span_imageₓ'. -/
 /-- `f` is an explicit argument so we can `apply` this theorem and obtain `h` as a new goal. -/
 theorem not_mem_span_of_apply_not_mem_span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) {x : M}
@@ -1104,7 +1060,7 @@ theorem supᵢ_span {ι : Sort _} (p : ι → Set M) : (⨆ i, span R (p i)) = s
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Set.unionᵢ.{u2, u3} M ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (p i))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Set.unionᵢ.{u1, u3} M ι (fun (i : ι) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (p i))))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Set.unionᵢ.{u1, u3} M ι (fun (i : ι) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (p i))))
 Case conversion may be inaccurate. Consider using '#align submodule.supr_eq_span Submodule.supᵢ_eq_spanₓ'. -/
 theorem supᵢ_eq_span {ι : Sort _} (p : ι → Submodule R M) : (⨆ i, p i) = span R (⋃ i, ↑(p i)) := by
   simp_rw [← supr_span, span_eq]
@@ -1141,7 +1097,7 @@ theorem supᵢ_toAddSubmonoid {ι : Sort _} (p : ι → Submodule R M) :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) {C : M -> Prop} {x : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> (forall (i : ι) (x : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (p i)) -> (C x)) -> (C (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))))))) -> (forall (x : M) (y : M), (C x) -> (C y) -> (C (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)))) x y))) -> (C x)
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) {C : M -> Prop} {x : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> (forall (i : ι) (x : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (p i)) -> (C x)) -> (C (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) -> (forall (x : M) (y : M), (C x) -> (C y) -> (C (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)))) x y))) -> (C x)
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) {C : M -> Prop} {x : M}, (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> (forall (i : ι) (x : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (p i)) -> (C x)) -> (C (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) -> (forall (x : M) (y : M), (C x) -> (C y) -> (C (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)))) x y))) -> (C x)
 Case conversion may be inaccurate. Consider using '#align submodule.supr_induction Submodule.supᵢ_inductionₓ'. -/
 /-- An induction principle for elements of `⨆ i, p i`.
 If `C` holds for `0` and all elements of `p i` for all `i`, and is preserved under addition,
@@ -1159,7 +1115,7 @@ theorem supᵢ_induction {ι : Sort _} (p : ι → Submodule R M) {C : M → Pro
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) {C : forall (x : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> Prop}, (forall (i : ι) (x : M) (H : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (p i)), C x (Submodule.mem_supᵢ_of_mem.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 ι x (fun (i : ι) => p i) i H)) -> (C (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)))))) (ZeroMemClass.zero_mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (AddSubmonoidClass.to_zeroMemClass.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)))) -> (forall (x : M) (y : M) (hx : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (hy : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))), (C x hx) -> (C y hy) -> (C (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)))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)) x y hx hy))) -> (forall {x : M} (hx : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))), C x hx)
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) {C : forall (x : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> Prop}, (forall (i : ι) (x : M) (H : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (p i)), C x (Submodule.mem_supᵢ_of_mem.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 ι x (fun (i : ι) => p i) i H)) -> (C (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)))) (ZeroMemClass.zero_mem.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (AddSubmonoidClass.toZeroMemClass.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.addSubmonoidClass.{u2, u1} R M _inst_1 _inst_2 _inst_3)) (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)))) -> (forall (x : M) (y : M) (hx : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (hy : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) y (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))), (C x hx) -> (C y hy) -> (C (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)))) x y) (AddMemClass.add_mem.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))) (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (AddSubmonoidClass.toAddMemClass.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.addSubmonoidClass.{u2, u1} R M _inst_1 _inst_2 _inst_3)) (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)) x y hx hy))) -> (forall {x : M} (hx : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))), C x hx)
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) {C : forall (x : M), (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) -> Prop}, (forall (i : ι) (x : M) (H : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (p i)), C x (Submodule.mem_supᵢ_of_mem.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 ι x (fun (i : ι) => p i) i H)) -> (C (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)))) (ZeroMemClass.zero_mem.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (AddSubmonoidClass.toZeroMemClass.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.addSubmonoidClass.{u2, u1} R M _inst_1 _inst_2 _inst_3)) (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)))) -> (forall (x : M) (y : M) (hx : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (hy : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) y (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))), (C x hx) -> (C y hy) -> (C (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)))) x y) (AddMemClass.add_mem.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))) (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (AddSubmonoidClass.toAddMemClass.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.addSubmonoidClass.{u2, u1} R M _inst_1 _inst_2 _inst_3)) (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i)) x y hx hy))) -> (forall {x : M} (hx : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))), C x hx)
 Case conversion may be inaccurate. Consider using '#align submodule.supr_induction' Submodule.supᵢ_induction'ₓ'. -/
 /-- A dependent version of `submodule.supr_induction`. -/
 @[elab_as_elim]
@@ -1180,7 +1136,7 @@ theorem supᵢ_induction' {ι : Sort _} (p : ι → Submodule R M) {C : ∀ x, (
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (m : M) (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), Iff (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) m)) p) (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m p)
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] (m : M) (p : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), Iff (LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) m)) p) (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m p)
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] (m : M) (p : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), Iff (LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) m)) p) (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m p)
 Case conversion may be inaccurate. Consider using '#align submodule.span_singleton_le_iff_mem Submodule.span_singleton_le_iff_memₓ'. -/
 @[simp]
 theorem span_singleton_le_iff_mem (m : M) (p : Submodule R M) : (R ∙ m) ≤ p ↔ m ∈ p := by
@@ -1232,7 +1188,7 @@ instance : IsCompactlyGenerated (Submodule R M) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p (SupSet.supₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (setOf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (T : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Exists.{succ u2} M (fun (m : M) => Exists.{0} (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m p) (fun (hm : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m p) => Exists.{0} (Ne.{succ u2} M m (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))))))) (fun (hz : Ne.{succ u2} M m (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 u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) T (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) m))))))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] (p : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) p (SupSet.supₛ.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) (setOf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (T : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Exists.{succ u1} M (fun (m : M) => Exists.{0} (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m p) (fun (hm : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m p) => Exists.{0} (Ne.{succ u1} M m (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) (fun (hz : Ne.{succ u1} M m (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) => Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) T (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) m))))))))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] (p : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) p (SupSet.supₛ.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) (setOf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (T : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Exists.{succ u1} M (fun (m : M) => Exists.{0} (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m p) (fun (hm : Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m p) => Exists.{0} (Ne.{succ u1} M m (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) (fun (hz : Ne.{succ u1} M m (OfNat.ofNat.{u1} M 0 (Zero.toOfNat0.{u1} M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2))))) => Eq.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) T (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) m))))))))
 Case conversion may be inaccurate. Consider using '#align submodule.submodule_eq_Sup_le_nonzero_spans Submodule.submodule_eq_supₛ_le_nonzero_spansₓ'. -/
 /-- A submodule is equal to the supremum of the spans of the submodule's nonzero elements. -/
 theorem submodule_eq_supₛ_le_nonzero_spans (p : Submodule R M) :
@@ -1254,7 +1210,7 @@ theorem submodule_eq_supₛ_le_nonzero_spans (p : Submodule R M) :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {a : M}, Iff (LT.lt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) I (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) I (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) a)))) (Not (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) a I))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {I : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3} {a : M}, Iff (LT.lt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) I (Sup.sup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) I (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) a)))) (Not (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) a I))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {I : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3} {a : M}, Iff (LT.lt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) I (Sup.sup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) I (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) a)))) (Not (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) a I))
 Case conversion may be inaccurate. Consider using '#align submodule.lt_sup_iff_not_mem Submodule.lt_sup_iff_not_memₓ'. -/
 theorem lt_sup_iff_not_mem {I : Submodule R M} {a : M} : (I < I ⊔ R ∙ a) ↔ a ∉ I :=
   by
@@ -1284,7 +1240,7 @@ theorem lt_sup_iff_not_mem {I : Submodule R M} {a : M} : (I < I ⊔ R ∙ a) ↔
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) {m : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (forall (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (forall (i : ι), LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (p i) N) -> (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) m N))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) {m : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (forall (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), (forall (i : ι), LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (p i) N) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m N))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} (p : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) {m : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι (fun (i : ι) => p i))) (forall (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), (forall (i : ι), LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (p i) N) -> (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) m N))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr Submodule.mem_supᵢₓ'. -/
 theorem mem_supᵢ {ι : Sort _} (p : ι → Submodule R M) {m : M} :
     (m ∈ ⨆ i, p i) ↔ ∀ N, (∀ i, p i ≤ N) → m ∈ N :=
@@ -1297,12 +1253,7 @@ section
 
 open Classical
 
-/- warning: submodule.mem_span_finite_of_mem_span -> Submodule.mem_span_finite_of_mem_span 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {S : Set.{u2} M} {x : M}, (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) -> (Exists.{succ u2} (Finset.{u2} M) (fun (T : Finset.{u2} M) => And (HasSubset.Subset.{u2} (Set.{u2} M) (Set.hasSubset.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} M) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} M) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} M) (Set.{u2} M) (Finset.Set.hasCoeT.{u2} M))) T) S) (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} M) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} M) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} M) (Set.{u2} M) (Finset.Set.hasCoeT.{u2} M))) T)))))
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {S : Set.{u2} M} {x : M}, (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 S)) -> (Exists.{succ u2} (Finset.{u2} M) (fun (T : Finset.{u2} M) => And (HasSubset.Subset.{u2} (Set.{u2} M) (Set.instHasSubsetSet.{u2} M) (Finset.toSet.{u2} M T) S) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Finset.toSet.{u2} M T)))))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_span_finite_of_mem_span Submodule.mem_span_finite_of_mem_spanₓ'. -/
+#print Submodule.mem_span_finite_of_mem_span /-
 /-- For every element in the span of a set, there exists a finite subset of the set
 such that the element is contained in the span of the subset. -/
 theorem mem_span_finite_of_mem_span {S : Set M} {x : M} (hx : x ∈ span R S) :
@@ -1324,6 +1275,7 @@ theorem mem_span_finite_of_mem_span {S : Set M} {x : M} (hx : x ∈ span R S) :
   · rintro a x ⟨T, hT, h2⟩
     exact ⟨T, hT, smul_mem _ _ h2⟩
 #align submodule.mem_span_finite_of_mem_span Submodule.mem_span_finite_of_mem_span
+-/
 
 end
 
@@ -1348,7 +1300,7 @@ def prod : Submodule R (M × M') :=
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {M' : Type.{u3}} [_inst_7 : AddCommMonoid.{u3} M'] [_inst_8 : Module.{u1, u3} R M' _inst_1 _inst_7] (q₁ : Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8), Eq.{succ (max u2 u3)} (Set.{max u2 u3} (Prod.{u2, u3} M M')) ((fun (a : Type.{max u2 u3}) (b : Type.{max u2 u3}) [self : HasLiftT.{succ (max u2 u3), succ (max u2 u3)} a b] => self.0) (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Set.{max u2 u3} (Prod.{u2, u3} M M')) (HasLiftT.mk.{succ (max u2 u3), succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Set.{max u2 u3} (Prod.{u2, u3} M M')) (CoeTCₓ.coe.{succ (max u2 u3), succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Set.{max u2 u3} (Prod.{u2, u3} M M')) (SetLike.Set.hasCoeT.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Prod.{u2, u3} M M') (Submodule.setLike.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8))))) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 p M' _inst_7 _inst_8 q₁)) (Set.prod.{u2, u3} M M' ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (Set.{u3} M') (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (Set.{u3} M') (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (Set.{u3} M') (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) M' (Submodule.setLike.{u1, u3} R M' _inst_1 _inst_7 _inst_8)))) q₁))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] (p : Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) {M' : Type.{u2}} [_inst_7 : AddCommMonoid.{u2} M'] [_inst_8 : Module.{u1, u2} R M' _inst_1 _inst_7] (q₁ : Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8), Eq.{max (succ u3) (succ u2)} (Set.{max u3 u2} (Prod.{u3, u2} M M')) (SetLike.coe.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Prod.{u3, u2} M M') (Submodule.instSetLikeSubmodule.{u1, max u3 u2} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Submodule.prod.{u1, u3, u2} R M _inst_1 _inst_2 _inst_3 p M' _inst_7 _inst_8 q₁)) (Set.prod.{u3, u2} M M' (SetLike.coe.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) p) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) M' (Submodule.instSetLikeSubmodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) q₁))
+  forall {R : Type.{u1}} {M : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] (p : Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) {M' : Type.{u2}} [_inst_7 : AddCommMonoid.{u2} M'] [_inst_8 : Module.{u1, u2} R M' _inst_1 _inst_7] (q₁ : Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8), Eq.{max (succ u3) (succ u2)} (Set.{max u3 u2} (Prod.{u3, u2} M M')) (SetLike.coe.{max u3 u2, max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Prod.{u3, u2} M M') (Submodule.setLike.{u1, max u3 u2} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Submodule.prod.{u1, u3, u2} R M _inst_1 _inst_2 _inst_3 p M' _inst_7 _inst_8 q₁)) (Set.prod.{u3, u2} M M' (SetLike.coe.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3) p) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) M' (Submodule.setLike.{u1, u2} R M' _inst_1 _inst_7 _inst_8) q₁))
 Case conversion may be inaccurate. Consider using '#align submodule.prod_coe Submodule.prod_coeₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
@@ -1360,7 +1312,7 @@ theorem prod_coe : (prod p q₁ : Set (M × M')) = p ×ˢ q₁ :=
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {M' : Type.{u3}} [_inst_7 : AddCommMonoid.{u3} M'] [_inst_8 : Module.{u1, u3} R M' _inst_1 _inst_7] {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {q : Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8} {x : Prod.{u2, u3} M M'}, Iff (Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} M M') (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (SetLike.hasMem.{max u2 u3, max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Prod.{u2, u3} M M') (Submodule.setLike.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8))) x (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 p M' _inst_7 _inst_8 q)) (And (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Prod.fst.{u2, u3} M M' x) p) (Membership.Mem.{u3, u3} M' (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) M' (Submodule.setLike.{u1, u3} R M' _inst_1 _inst_7 _inst_8)) (Prod.snd.{u2, u3} M M' x) q))
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {M' : Type.{u1}} [_inst_7 : AddCommMonoid.{u1} M'] [_inst_8 : Module.{u3, u1} R M' _inst_1 _inst_7] {p : Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_3} {q : Submodule.{u3, u1} R M' _inst_1 _inst_7 _inst_8} {x : Prod.{u2, u1} M M'}, Iff (Membership.mem.{max u2 u1, max u2 u1} (Prod.{u2, u1} M M') (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u1} M M' _inst_2 _inst_7) (Prod.module.{u3, u2, u1} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u1} M M' _inst_2 _inst_7) (Prod.module.{u3, u2, u1} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Prod.{u2, u1} M M') (Submodule.instSetLikeSubmodule.{u3, max u2 u1} R (Prod.{u2, u1} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u1} M M' _inst_2 _inst_7) (Prod.module.{u3, u2, u1} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8))) x (Submodule.prod.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 p M' _inst_7 _inst_8 q)) (And (Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u3, u2} R M _inst_1 _inst_2 _inst_3)) (Prod.fst.{u2, u1} M M' x) p) (Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' _inst_1 _inst_7 _inst_8) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' _inst_1 _inst_7 _inst_8) M' (Submodule.instSetLikeSubmodule.{u3, u1} R M' _inst_1 _inst_7 _inst_8)) (Prod.snd.{u2, u1} M M' x) q))
+  forall {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M _inst_1 _inst_2] {M' : Type.{u1}} [_inst_7 : AddCommMonoid.{u1} M'] [_inst_8 : Module.{u3, u1} R M' _inst_1 _inst_7] {p : Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_3} {q : Submodule.{u3, u1} R M' _inst_1 _inst_7 _inst_8} {x : Prod.{u2, u1} M M'}, Iff (Membership.mem.{max u2 u1, max u2 u1} (Prod.{u2, u1} M M') (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u1} M M' _inst_2 _inst_7) (Prod.module.{u3, u2, u1} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submodule.{u3, max u1 u2} R (Prod.{u2, u1} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u1} M M' _inst_2 _inst_7) (Prod.module.{u3, u2, u1} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Prod.{u2, u1} M M') (Submodule.setLike.{u3, max u2 u1} R (Prod.{u2, u1} M M') _inst_1 (Prod.instAddCommMonoidSum.{u2, u1} M M' _inst_2 _inst_7) (Prod.module.{u3, u2, u1} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8))) x (Submodule.prod.{u3, u2, u1} R M _inst_1 _inst_2 _inst_3 p M' _inst_7 _inst_8 q)) (And (Membership.mem.{u2, u2} M (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u3, u2} R M _inst_1 _inst_2 _inst_3)) (Prod.fst.{u2, u1} M M' x) p) (Membership.mem.{u1, u1} M' (Submodule.{u3, u1} R M' _inst_1 _inst_7 _inst_8) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R M' _inst_1 _inst_7 _inst_8) M' (Submodule.setLike.{u3, u1} R M' _inst_1 _inst_7 _inst_8)) (Prod.snd.{u2, u1} M M' x) q))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_prod Submodule.mem_prodₓ'. -/
 @[simp]
 theorem mem_prod {p : Submodule R M} {q : Submodule R M'} {x : M × M'} :
@@ -1463,7 +1415,7 @@ theorem span_neg (s : Set M) : span R (-s) = span R s :=
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {x : M} {y : M} {s : Set.{u2} M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Insert.insert.{u2, u2} M (Set.{u2} M) (Set.hasInsert.{u2} M) y s))) (Exists.{succ u1} R (fun (a : R) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))))) x (SMul.smul.{u1, u2} R M (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{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 (Ring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) a y)) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 s)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {x : M} {y : M} {s : Set.{u2} M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Insert.insert.{u2, u2} M (Set.{u2} M) (Set.instInsertSet.{u2} M) y s))) (Exists.{succ u1} R (fun (a : R) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))))) x (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_2))))) (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_2))))) (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_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) a y)) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 s)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {x : M} {y : M} {s : Set.{u2} M}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Insert.insert.{u2, u2} M (Set.{u2} M) (Set.instInsertSet.{u2} M) y s))) (Exists.{succ u1} R (fun (a : R) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)))))) x (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_2))))) (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_2))))) (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_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) a y)) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 s)))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_span_insert' Submodule.mem_span_insert'ₓ'. -/
 theorem mem_span_insert' {x y} {s : Set M} :
     x ∈ span R (insert y s) ↔ ∃ a : R, x + a • y ∈ span R s :=
@@ -1654,7 +1606,7 @@ variable {σ₁₂ : R →+* R₂}
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u3} M} {f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (forall {{x : M}}, (Membership.Mem.{u3, u3} M (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g x)))
 but is expected to have type
-  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (forall {{x : M}}, (Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u3, u4} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g x)))
+  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (forall {{x : M}}, (Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u3, u4} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g x)))
 Case conversion may be inaccurate. Consider using '#align linear_map.eq_on_span LinearMap.eqOn_spanₓ'. -/
 /-- If two linear maps are equal on a set `s`, then they are equal on `submodule.span s`.
 
@@ -1667,7 +1619,7 @@ theorem eqOn_span {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (H : Set.EqOn f
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u3} M} {f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Set.EqOn.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)))
 but is expected to have type
-  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) (SetLike.coe.{u4, u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s)))
+  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) (SetLike.coe.{u4, u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s)))
 Case conversion may be inaccurate. Consider using '#align linear_map.eq_on_span' LinearMap.eqOn_span'ₓ'. -/
 /-- If two linear maps are equal on a set `s`, then they are equal on `submodule.span s`.
 
@@ -1774,7 +1726,7 @@ variable (K V) [Field K] [AddCommGroup V] [Module K V]
 lean 3 declaration is
   forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (LinearEquiv.{u1, u1, u1, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} K _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} K _inst_1) K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))
+  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.to_span_nonzero_singleton LinearEquiv.toSpanNonzeroSingletonₓ'. -/
 /-- Given a nonzero element `x` of a vector space `V` over a field `K`, the natural
     map from `K` to the span of `x`, with invertibility check to consider it as an
@@ -1790,7 +1742,7 @@ def toSpanNonzeroSingleton (x : V) (h : x ≠ 0) : K ≃ₗ[K] K ∙ x :=
 lean 3 declaration is
   forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearEquiv.{u1, u1, u1, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} K _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} K _inst_1) K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)))) (fun (_x : LinearEquiv.{u1, u1, u1, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} K _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} K _inst_1) K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)))) => K -> (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)))) (LinearEquiv.hasCoeToFun.{u1, u1, u1, u2} K K K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.toSpanNonzeroSingleton._proof_1.{u1} K _inst_1) (LinearEquiv.toSpanNonzeroSingleton._proof_2.{u1} K _inst_1)) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (NonAssocRing.toAddGroupWithOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.Mem.{u2, u2} V (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1))))) (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K 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(Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V 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(LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K 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(DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u2} K K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))
+  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : K) => Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1))))) (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u1, u2} (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u2, max u1 u2} K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u2, max u1 u2} K K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (LinearEquiv.{u1, u1, u1, u2} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u2} K K K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))))) (LinearEquiv.toSpanNonzeroSingleton.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (OfNat.ofNat.{u1} K 1 (One.toOfNat1.{u1} K (Semiring.toOne.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))))) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.to_span_nonzero_singleton_one LinearEquiv.toSpanNonzeroSingleton_oneₓ'. -/
 theorem toSpanNonzeroSingleton_one (x : V) (h : x ≠ 0) :
     LinearEquiv.toSpanNonzeroSingleton K V x h 1 =
@@ -1805,7 +1757,7 @@ theorem toSpanNonzeroSingleton_one (x : V) (h : x ≠ 0) :
 lean 3 declaration is
   forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) K (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1))
+  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V), (Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))) -> (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.coord LinearEquiv.coordₓ'. -/
 /-- Given a nonzero element `x` of a vector space `V` over a field `K`, the natural map
     from the span of `x` to `K`.-/
@@ -1817,7 +1769,7 @@ abbrev coord (x : V) (h : x ≠ 0) : (K ∙ x) ≃ₗ[K] K :=
 lean 3 declaration is
   forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))))))))), Eq.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) K (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) K (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) => 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(Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearEquiv.coord._proof_1.{u1} K _inst_1) (LinearEquiv.coord._proof_2.{u1} K _inst_1)) (LinearEquiv.coord.{u1, u2} K V _inst_1 _inst_2 _inst_3 x h) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.Mem.{u2, u2} V (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (OfNat.ofNat.{u1} K 1 (OfNat.mk.{u1} K 1 (One.one.{u1} K (AddMonoidWithOne.toOne.{u1} K (AddGroupWithOne.toAddMonoidWithOne.{u1} K (NonAssocRing.toAddGroupWithOne.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))))))
 but is expected to have type
-  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K 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(Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V 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(Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (fun (_x : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (SMulZeroClass.toSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toZero.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K 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(Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.instModuleSubtypeMemSubmoduleInstMembershipInstSetLikeSubmoduleInstAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u1, max u1 u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.instAddCommMonoidSubtypeMemSubmoduleInstMembershipInstSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K 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(AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) 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u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) 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(AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.instSetLikeSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K 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+  forall (K : Type.{u1}) (V : Type.{u2}) [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (x : V) (h : Ne.{succ u2} V x (OfNat.ofNat.{u2} V 0 (Zero.toOfNat0.{u2} V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_2)))))))), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K 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(Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribSMul.toSMulZeroClass.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddMonoid.toAddZeroClass.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))) (DistribMulAction.toDistribSMul.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))))))) (SMulZeroClass.toSMul.{u1, u1} K K (AddMonoid.toZero.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} K K (AddMonoid.toAddZeroClass.{u1} K (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} K K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, u2, u1} (LinearEquiv.{u1, u1, u2, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (MonoidWithZero.toMonoid.{u1} K (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (AddCommMonoid.toAddMonoid.{u2} (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (AddCommMonoid.toAddMonoid.{u1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1))))))) (Module.toDistribMulAction.{u1, u2} K (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) (Module.toDistribMulAction.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u1, max 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(DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} 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(Field.toSemifield.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (RingHomInvPair.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)))) (Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) K (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonUnitalRing.toNonUnitalNonAssocRing.{u1} K (NonUnitalCommRing.toNonUnitalRing.{u1} K (CommRing.toNonUnitalCommRing.{u1} K (Field.toCommRing.{u1} K _inst_1)))))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K 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(Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x)))) => K) (Subtype.mk.{succ u2} V (fun (x_1 : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x_1 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) x))) x (Submodule.mem_span_singleton_self.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 x))) _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.coord_self LinearEquiv.coord_selfₓ'. -/
 theorem coord_self (x : V) (h : x ≠ 0) :
     (coord K V x h) (⟨x, Submodule.mem_span_singleton_self x⟩ : K ∙ x) = 1 := by

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

@@ -540,7 +540,7 @@ theorem span_smul_eq_of_isUnit (s : Set M) (r : R) (hr : IsUnit r) : span R (r 
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} [hι : Nonempty.{u3} ι] (S : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Directed.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) S) -> (Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u2, u3} M ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (S i))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} [hι : Nonempty.{u3} ι] (S : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), (Directed.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.5715 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.5717 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.5715 x._@.Mathlib.LinearAlgebra.Span._hyg.5717) S) -> (Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u1, u3} M ι (fun (i : ι) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (S i))))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} [hι : Nonempty.{u3} ι] (S : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), (Directed.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.5760 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.5762 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.5760 x._@.Mathlib.LinearAlgebra.Span._hyg.5762) S) -> (Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u1, u3} M ι (fun (i : ι) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (S i))))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_supr_of_directed Submodule.coe_supᵢ_of_directedₓ'. -/
 @[simp]
 theorem coe_supᵢ_of_directed {ι} [hι : Nonempty ι] (S : ι → Submodule R M)
@@ -561,7 +561,7 @@ theorem coe_supᵢ_of_directed {ι} [hι : Nonempty ι] (S : ι → Submodule R
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} [_inst_7 : Nonempty.{u3} ι] (S : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Directed.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) S) -> (forall {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι S)) (Exists.{u3} ι (fun (i : ι) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (S i))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} [_inst_7 : Nonempty.{u3} ι] (S : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), (Directed.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.6013 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.6015 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.6013 x._@.Mathlib.LinearAlgebra.Span._hyg.6015) S) -> (forall {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι S)) (Exists.{u3} ι (fun (i : ι) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (S i))))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} [_inst_7 : Nonempty.{u3} ι] (S : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), (Directed.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.6058 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.6060 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.6058 x._@.Mathlib.LinearAlgebra.Span._hyg.6060) S) -> (forall {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι S)) (Exists.{u3} ι (fun (i : ι) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (S i))))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_of_directed Submodule.mem_supᵢ_of_directedₓ'. -/
 @[simp]
 theorem mem_supᵢ_of_directed {ι} [Nonempty ι] (S : ι → Submodule R M) (H : Directed (· ≤ ·) S) {x} :
@@ -575,7 +575,7 @@ theorem mem_supᵢ_of_directed {ι} [Nonempty ι] (S : ι → Submodule R M) (H
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {z : M}, (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) s) -> (DirectedOn.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) s) -> (Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (SupSet.supₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) s)) (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (y : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Exists.{0} (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) (fun (H : Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z y))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {z : M}, (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) s) -> (DirectedOn.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.6146 : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.6148 : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.6146 x._@.Mathlib.LinearAlgebra.Span._hyg.6148) s) -> (Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (SupSet.supₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) s)) (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (y : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => And (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z y))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {z : M}, (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) s) -> (DirectedOn.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.6191 : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.6193 : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.6191 x._@.Mathlib.LinearAlgebra.Span._hyg.6193) s) -> (Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (SupSet.supₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) s)) (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (y : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => And (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z y))))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_Sup_of_directed Submodule.mem_supₛ_of_directedₓ'. -/
 theorem mem_supₛ_of_directed {s : Set (Submodule R M)} {z} (hs : s.Nonempty)
     (hdir : DirectedOn (· ≤ ·) s) : z ∈ supₛ s ↔ ∃ y ∈ s, z ∈ y :=

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

@@ -157,7 +157,7 @@ theorem span_coe_eq_restrictScalars [Semiring S] [SMul S R] [Module S M] [IsScal
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u3} M), Eq.{succ u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s))
 Case conversion may be inaccurate. Consider using '#align submodule.map_span Submodule.map_spanₓ'. -/
 theorem map_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (s : Set M) :
     (span R s).map f = span R₂ (f '' s) :=
@@ -170,7 +170,7 @@ theorem map_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u3} M), Eq.{succ u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s))
 Case conversion may be inaccurate. Consider using '#align linear_map.map_span LinearMap.map_spanₓ'. -/
 alias Submodule.map_span ← _root_.linear_map.map_span
 #align linear_map.map_span LinearMap.map_span
@@ -179,7 +179,7 @@ alias Submodule.map_span ← _root_.linear_map.map_span
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u3} M) (N : Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)))) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) m s) -> (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M) (N : Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) m s) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) m) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.instSetLikeSubmodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M) (N : Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) m s) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) m) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.instSetLikeSubmodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 Case conversion may be inaccurate. Consider using '#align submodule.map_span_le Submodule.map_span_leₓ'. -/
 theorem map_span_le [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (s : Set M) (N : Submodule R₂ M₂) :
     map f (span R s) ≤ N ↔ ∀ m ∈ s, f m ∈ N :=
@@ -192,7 +192,7 @@ theorem map_span_le [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u3} M) (N : Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)))) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.Mem.{u3, u3} M (Set.{u3} M) (Set.hasMem.{u3} M) m s) -> (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M) (N : Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) m s) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) m) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.instSetLikeSubmodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u2} M) (N : Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6), Iff (LE.le.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.completeLattice.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6))))) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) N) (forall (m : M), (Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) m s) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) m) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.instSetLikeSubmodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f m) N))
 Case conversion may be inaccurate. Consider using '#align linear_map.map_span_le LinearMap.map_span_leₓ'. -/
 alias Submodule.map_span_le ← _root_.linear_map.map_span_le
 #align linear_map.map_span_le LinearMap.map_span_le
@@ -215,7 +215,7 @@ theorem span_insert_zero : span R (insert (0 : M) s) = span R s :=
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u4} M₂), LE.le.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u1} M₂), LE.le.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u4, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u1} M₂), LE.le.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u4, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
 Case conversion may be inaccurate. Consider using '#align submodule.span_preimage_le Submodule.span_preimage_leₓ'. -/
 -- See also `span_preimage_eq` below.
 theorem span_preimage_le (f : M →ₛₗ[σ₁₂] M₂) (s : Set M₂) :
@@ -229,7 +229,7 @@ theorem span_preimage_le (f : M →ₛₗ[σ₁₂] M₂) (s : Set M₂) :
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u4} M₂), LE.le.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u1} M₂), LE.le.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u4, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (s : Set.{u1} M₂), LE.le.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u4, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.preimage.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.comap.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 s))
 Case conversion may be inaccurate. Consider using '#align linear_map.span_preimage_le LinearMap.span_preimage_leₓ'. -/
 alias Submodule.span_preimage_le ← _root_.linear_map.span_preimage_le
 #align linear_map.span_preimage_le LinearMap.span_preimage_le
@@ -540,7 +540,7 @@ theorem span_smul_eq_of_isUnit (s : Set M) (r : R) (hr : IsUnit r) : span R (r 
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} [hι : Nonempty.{u3} ι] (S : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Directed.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) S) -> (Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u2, u3} M ι (fun (i : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (S i))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} [hι : Nonempty.{u3} ι] (S : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), (Directed.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.5711 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.5713 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.5711 x._@.Mathlib.LinearAlgebra.Span._hyg.5713) S) -> (Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u1, u3} M ι (fun (i : ι) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (S i))))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} [hι : Nonempty.{u3} ι] (S : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), (Directed.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.5715 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.5717 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.5715 x._@.Mathlib.LinearAlgebra.Span._hyg.5717) S) -> (Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι S)) (Set.unionᵢ.{u1, u3} M ι (fun (i : ι) => SetLike.coe.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (S i))))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_supr_of_directed Submodule.coe_supᵢ_of_directedₓ'. -/
 @[simp]
 theorem coe_supᵢ_of_directed {ι} [hι : Nonempty ι] (S : ι → Submodule R M)
@@ -561,7 +561,7 @@ theorem coe_supᵢ_of_directed {ι} [hι : Nonempty ι] (S : ι → Submodule R
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {ι : Sort.{u3}} [_inst_7 : Nonempty.{u3} ι] (S : ι -> (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Directed.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) ι (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) S) -> (forall {x : M}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u2, u3} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) ι S)) (Exists.{u3} ι (fun (i : ι) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (S i))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} [_inst_7 : Nonempty.{u3} ι] (S : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), (Directed.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.6009 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.6011 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.6009 x._@.Mathlib.LinearAlgebra.Span._hyg.6011) S) -> (forall {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι S)) (Exists.{u3} ι (fun (i : ι) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (S i))))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {ι : Sort.{u3}} [_inst_7 : Nonempty.{u3} ι] (S : ι -> (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)), (Directed.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) ι (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.6013 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.6015 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.6013 x._@.Mathlib.LinearAlgebra.Span._hyg.6015) S) -> (forall {x : M}, Iff (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (supᵢ.{u1, u3} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))) ι S)) (Exists.{u3} ι (fun (i : ι) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x (S i))))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_supr_of_directed Submodule.mem_supᵢ_of_directedₓ'. -/
 @[simp]
 theorem mem_supᵢ_of_directed {ι} [Nonempty ι] (S : ι → Submodule R M) (H : Directed (· ≤ ·) S) {x} :
@@ -575,7 +575,7 @@ theorem mem_supᵢ_of_directed {ι} [Nonempty ι] (S : ι → Submodule R M) (H
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {z : M}, (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) s) -> (DirectedOn.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) s) -> (Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (SupSet.supₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) s)) (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (y : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Exists.{0} (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) (fun (H : Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z y))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {z : M}, (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) s) -> (DirectedOn.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.6142 : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.6144 : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.6142 x._@.Mathlib.LinearAlgebra.Span._hyg.6144) s) -> (Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (SupSet.supₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) s)) (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (y : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => And (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z y))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)} {z : M}, (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) s) -> (DirectedOn.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (x._@.Mathlib.LinearAlgebra.Span._hyg.6146 : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.LinearAlgebra.Span._hyg.6148 : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.LinearAlgebra.Span._hyg.6146 x._@.Mathlib.LinearAlgebra.Span._hyg.6148) s) -> (Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z (SupSet.supₛ.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toSupSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))) s)) (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (y : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => And (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y s) (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z y))))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_Sup_of_directed Submodule.mem_supₛ_of_directedₓ'. -/
 theorem mem_supₛ_of_directed {s : Set (Submodule R M)} {z} (hs : s.Nonempty)
     (hdir : DirectedOn (· ≤ ·) s) : z ∈ supₛ s ↔ ∃ y ∈ s, z ∈ y :=
@@ -1045,7 +1045,7 @@ theorem span_singleton_eq_span_singleton {R M : Type _} [Ring R] [AddCommGroup M
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] {s : Set.{u3} M} [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6), Eq.{succ u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.map.{u1, u2, u3, u4, max u3 u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] {s : Set.{u2} M} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] {s : Set.{u2} M} [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6), Eq.{succ u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)) (Submodule.map.{u4, u3, u2, u1, max u2 u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂ _inst_7 (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s))
 Case conversion may be inaccurate. Consider using '#align submodule.span_image Submodule.span_imageₓ'. -/
 @[simp]
 theorem span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) :
@@ -1057,7 +1057,7 @@ theorem span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂)
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u3} M}, (Membership.Mem.{u3, u3} M (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) -> (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u2} M}, (Membership.mem.{u2, u2} M (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u4, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) x) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.instSetLikeSubmodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u2} M}, (Membership.mem.{u2, u2} M (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u4, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.instSetLikeSubmodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))
 Case conversion may be inaccurate. Consider using '#align submodule.apply_mem_span_image_of_mem_span Submodule.apply_mem_span_image_of_mem_spanₓ'. -/
 theorem apply_mem_span_image_of_mem_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) {x : M}
     {s : Set M} (h : x ∈ Submodule.span R s) : f x ∈ Submodule.span R₂ (f '' s) :=
@@ -1081,7 +1081,7 @@ theorem map_subtype_span_singleton {p : Submodule R M} (x : p) :
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u3} M}, (Not (Membership.Mem.{u4, u4} M₂ (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u2, u4} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))) -> (Not (Membership.Mem.{u3, u3} M (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)))
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u2} M}, (Not (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) x) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.instSetLikeSubmodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))) -> (Not (Membership.mem.{u2, u2} M (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u4, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)))
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] [_inst_7 : RingHomSurjective.{u4, u3} R R₂ _inst_1 _inst_4 σ₁₂] (f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) {x : M} {s : Set.{u2} M}, (Not (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (Submodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6) M₂ (Submodule.instSetLikeSubmodule.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (Submodule.span.{u3, u1} R₂ M₂ _inst_4 _inst_5 _inst_6 (Set.image.{u2, u1} M M₂ (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) s)))) -> (Not (Membership.mem.{u2, u2} M (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u4, u2} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 s)))
 Case conversion may be inaccurate. Consider using '#align submodule.not_mem_span_of_apply_not_mem_span_image Submodule.not_mem_span_of_apply_not_mem_span_imageₓ'. -/
 /-- `f` is an explicit argument so we can `apply` this theorem and obtain `h` as a new goal. -/
 theorem not_mem_span_of_apply_not_mem_span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) {x : M}
@@ -1620,7 +1620,7 @@ theorem span_singleton_eq_range (x : M) : (R ∙ x) = (toSpanSingleton R M x).ra
 lean 3 declaration is
   forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (x : M), Eq.{succ u2} M (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3) (fun (_x : LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3) => R -> M) (LinearMap.hasCoeToFun.{u1, u1, u1, u2} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.toSpanSingleton.{u1, u2} R M _inst_1 _inst_2 _inst_3 x) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) x
 but is expected to have type
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => M) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u2} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.toSpanSingleton.{u1, u2} R M _inst_1 _inst_2 _inst_3 x) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) x
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (x : M), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => M) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u1, u1, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u2} R R R M _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) _inst_2 (Semiring.toModule.{u1} R _inst_1) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.toSpanSingleton.{u1, u2} R M _inst_1 _inst_2 _inst_3 x) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) x
 Case conversion may be inaccurate. Consider using '#align linear_map.to_span_singleton_one LinearMap.toSpanSingleton_oneₓ'. -/
 @[simp]
 theorem toSpanSingleton_one (x : M) : toSpanSingleton R M x 1 = x :=
@@ -1654,7 +1654,7 @@ variable {σ₁₂ : R →+* R₂}
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u3} M} {f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (forall {{x : M}}, (Membership.Mem.{u3, u3} M (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g x)))
 but is expected to have type
-  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (forall {{x : M}}, (Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u3, u4} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g x)))
+  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (forall {{x : M}}, (Membership.mem.{u4, u4} M (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u4, u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u3, u4} R M _inst_1 _inst_2 _inst_3)) x (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s)) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f x) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g x)))
 Case conversion may be inaccurate. Consider using '#align linear_map.eq_on_span LinearMap.eqOn_spanₓ'. -/
 /-- If two linear maps are equal on a set `s`, then they are equal on `submodule.span s`.
 
@@ -1667,7 +1667,7 @@ theorem eqOn_span {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (H : Set.EqOn f
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u3} M} {f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Set.EqOn.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Set.{u3} M) (HasLiftT.mk.{succ u3, succ u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Set.{u3} M) (CoeTCₓ.coe.{succ u3, succ u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Set.{u3} M) (SetLike.Set.hasCoeT.{u3, u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u3} R M _inst_1 _inst_2 _inst_3)))) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s)))
 but is expected to have type
-  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) (SetLike.coe.{u4, u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s)))
+  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) (SetLike.coe.{u4, u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s)))
 Case conversion may be inaccurate. Consider using '#align linear_map.eq_on_span' LinearMap.eqOn_span'ₓ'. -/
 /-- If two linear maps are equal on a set `s`, then they are equal on `submodule.span s`.
 
@@ -1682,7 +1682,7 @@ theorem eqOn_span' {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (H : Set.EqOn
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u3} M} {f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Eq.{succ u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 s) (Top.top.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.hasTop.{u1, u3} R M _inst_1 _inst_2 _inst_3))) -> (Set.EqOn.{u3, u4} M M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Eq.{max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) f g)
 but is expected to have type
-  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Eq.{succ u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s) (Top.top.{u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.instTopSubmodule.{u3, u4} R M _inst_1 _inst_2 _inst_3))) -> (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Eq.{max (succ u4) (succ u1)} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) f g)
+  forall {R : Type.{u3}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u3, u2} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {s : Set.{u4} M} {f : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Eq.{succ u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u3, u4} R M _inst_1 _inst_2 _inst_3 s) (Top.top.{u4} (Submodule.{u3, u4} R M _inst_1 _inst_2 _inst_3) (Submodule.instTopSubmodule.{u3, u4} R M _inst_1 _inst_2 _inst_3))) -> (Set.EqOn.{u4, u1} M M₂ (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f) (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u3, u2, u4, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g) s) -> (Eq.{max (succ u4) (succ u1)} (LinearMap.{u3, u2, u4, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) f g)
 Case conversion may be inaccurate. Consider using '#align linear_map.ext_on LinearMap.ext_onₓ'. -/
 /-- If `s` generates the whole module and linear maps `f`, `g` are equal on `s`, then they are
 equal. -/
@@ -1694,7 +1694,7 @@ theorem ext_on {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (hv : span R s = 
 lean 3 declaration is
   forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u2} R₂] [_inst_5 : AddCommMonoid.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_4)} {ι : Type.{u5}} {v : ι -> M} {f : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Eq.{succ u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u3} R M _inst_1 _inst_2 _inst_3 (Set.range.{u3, succ u5} M ι v)) (Top.top.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.hasTop.{u1, u3} R M _inst_1 _inst_2 _inst_3))) -> (forall (i : ι), Eq.{succ u4} M₂ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (v i)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) (fun (_x : LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) => M -> M₂) (LinearMap.hasCoeToFun.{u1, u2, u3, u4} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g (v i))) -> (Eq.{max (succ u3) (succ u4)} (LinearMap.{u1, u2, u3, u4} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) f g)
 but is expected to have type
-  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} {ι : Type.{u5}} {v : ι -> M} {f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Eq.{succ u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.range.{u2, succ u5} M ι v)) (Top.top.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.instTopSubmodule.{u4, u2} R M _inst_1 _inst_2 _inst_3))) -> (forall (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) (v i)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (v i)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g (v i))) -> (Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) f g)
+  forall {R : Type.{u4}} {R₂ : Type.{u3}} {M : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : Semiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u4, u2} R M _inst_1 _inst_2] [_inst_4 : Semiring.{u3} R₂] [_inst_5 : AddCommMonoid.{u1} M₂] [_inst_6 : Module.{u3, u1} R₂ M₂ _inst_4 _inst_5] {σ₁₂ : RingHom.{u4, u3} R R₂ (Semiring.toNonAssocSemiring.{u4} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_4)} {ι : Type.{u5}} {v : ι -> M} {f : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6} {g : LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6}, (Eq.{succ u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u4, u2} R M _inst_1 _inst_2 _inst_3 (Set.range.{u2, succ u5} M ι v)) (Top.top.{u2} (Submodule.{u4, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.instTopSubmodule.{u4, u2} R M _inst_1 _inst_2 _inst_3))) -> (forall (i : ι), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) (v i)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) f (v i)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₂) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u2, u1} R R₂ M M₂ _inst_1 _inst_4 _inst_2 _inst_5 _inst_3 _inst_6 σ₁₂) g (v i))) -> (Eq.{max (succ u2) (succ u1)} (LinearMap.{u4, u3, u2, u1} R R₂ _inst_1 _inst_4 σ₁₂ M M₂ _inst_2 _inst_5 _inst_3 _inst_6) f g)
 Case conversion may be inaccurate. Consider using '#align linear_map.ext_on_range LinearMap.ext_on_rangeₓ'. -/
 /-- If the range of `v : ι → M` generates the whole module and linear maps `f`, `g` are equal at
 each `v i`, then they are equal. -/
@@ -1717,7 +1717,7 @@ open Classical
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (f : LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) {x : V}, (Ne.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) => V -> K) (LinearMap.hasCoeToFun.{u1, u1, u2, u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f x) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)) (LinearMap.ker.{u1, u1, u2, u1, max u2 u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.semilinearMapClass.{u1, u1, u2, u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f)) (Top.top.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))
 but is expected to have type
-  forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] (f : LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1)) {x : V}, (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1)) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) (CommGroupWithZero.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) (Semifield.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) _inst_1))))))) -> (Eq.{succ u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Sup.sup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Submodule.span.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3 (Singleton.singleton.{u1, u1} V (Set.{u1} V) (Set.instSingletonSet.{u1} V) x)) (LinearMap.ker.{u2, u2, u1, u2, max u2 u1} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f)) (Top.top.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3)))
+  forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] (f : LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1)) {x : V}, (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1)) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (CommGroupWithZero.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (Semifield.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => K) x) _inst_1))))))) -> (Eq.{succ u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Sup.sup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Submodule.span.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3 (Singleton.singleton.{u1, u1} V (Set.{u1} V) (Set.instSingletonSet.{u1} V) x)) (LinearMap.ker.{u2, u2, u1, u2, max u2 u1} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f)) (Top.top.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3)))
 Case conversion may be inaccurate. Consider using '#align linear_map.span_singleton_sup_ker_eq_top LinearMap.span_singleton_sup_ker_eq_topₓ'. -/
 theorem span_singleton_sup_ker_eq_top (f : V →ₗ[K] K) {x : V} (hx : f x ≠ 0) :
     (K ∙ x) ⊔ f.ker = ⊤ :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

@@ -413,9 +413,9 @@ theorem span_univ : span R (univ : Set M) = ⊤ :=
 
 /- warning: submodule.span_union -> Submodule.span_union 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (s : Set.{u2} M) (t : Set.{u2} M), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Union.union.{u2} (Set.{u2} M) (Set.hasUnion.{u2} M) s t)) (HasSup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 t))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (s : Set.{u2} M) (t : Set.{u2} M), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Union.union.{u2} (Set.{u2} M) (Set.hasUnion.{u2} M) s t)) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 t))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (s : Set.{u2} M) (t : Set.{u2} M), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Union.union.{u2} (Set.{u2} M) (Set.instUnionSet.{u2} M) s t)) (HasSup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 t))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (s : Set.{u2} M) (t : Set.{u2} M), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Union.union.{u2} (Set.{u2} M) (Set.instUnionSet.{u2} M) s t)) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 t))
 Case conversion may be inaccurate. Consider using '#align submodule.span_union Submodule.span_unionₓ'. -/
 theorem span_union (s t : Set M) : span R (s ∪ t) = span R s ⊔ span R t :=
   (Submodule.gi R M).gc.l_sup
@@ -456,18 +456,18 @@ theorem span_attach_bunionᵢ [DecidableEq M] {α : Type _} (s : Finset α) (f :
 
 /- warning: submodule.sup_span -> Submodule.sup_span 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (HasSup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Union.union.{u2} (Set.{u2} M) (Set.hasUnion.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p) s))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Union.union.{u2} (Set.{u2} M) (Set.hasUnion.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p) 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (HasSup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Union.union.{u2} (Set.{u2} M) (Set.instUnionSet.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) s))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Union.union.{u2} (Set.{u2} M) (Set.instUnionSet.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) s))
 Case conversion may be inaccurate. Consider using '#align submodule.sup_span Submodule.sup_spanₓ'. -/
 theorem sup_span : p ⊔ span R s = span R (p ∪ s) := by rw [Submodule.span_union, p.span_eq]
 #align submodule.sup_span Submodule.sup_span
 
 /- warning: submodule.span_sup -> Submodule.span_sup 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (HasSup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) p) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Union.union.{u2} (Set.{u2} M) (Set.hasUnion.{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 _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) p) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Union.union.{u2} (Set.{u2} M) (Set.hasUnion.{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 _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (HasSup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) p) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Union.union.{u2} (Set.{u2} M) (Set.instUnionSet.{u2} M) s (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {s : Set.{u2} M}, Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s) p) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Union.union.{u2} (Set.{u2} M) (Set.instUnionSet.{u2} M) s (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p)))
 Case conversion may be inaccurate. Consider using '#align submodule.span_sup Submodule.span_supₓ'. -/
 theorem span_sup : span R s ⊔ p = span R (s ∪ p) := by rw [Submodule.span_union, p.span_eq]
 #align submodule.span_sup Submodule.span_sup
@@ -625,9 +625,9 @@ variable {p p'}
 
 /- warning: submodule.mem_sup -> Submodule.mem_sup is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (Exists.{succ u2} M (fun (y : M) => Exists.{0} (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y p) (fun (H : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y p) => Exists.{succ u2} M (fun (z : M) => Exists.{0} (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z p') (fun (H : Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z p') => 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)))) y z) x)))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (HasSup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (Exists.{succ u2} M (fun (y : M) => And (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y p) (Exists.{succ u2} M (fun (z : M) => And (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z p') (Eq.{succ u2} M (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) y z) x)))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (Exists.{succ u2} M (fun (y : M) => And (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) y p) (Exists.{succ u2} M (fun (z : M) => And (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) z p') (Eq.{succ u2} M (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) y z) x)))))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_sup Submodule.mem_supₓ'. -/
 theorem mem_sup : x ∈ p ⊔ p' ↔ ∃ y ∈ p, ∃ z ∈ p', y + z = x :=
   ⟨fun h => by
@@ -647,9 +647,9 @@ theorem mem_sup : x ∈ p ⊔ p' ↔ ∃ y ∈ p, ∃ z ∈ p', y + z = x :=
 
 /- warning: submodule.mem_sup' -> Submodule.mem_sup' is a dubious translation:
 lean 3 declaration is
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+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3}, Iff (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (Exists.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) (fun (y : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) => Exists.{succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p') (fun (z : coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p') => 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)))) ((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_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p))))) y) ((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_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p') M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p') M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p') M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) p') M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p'))))) z)) x)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (HasSup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (Exists.{succ u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p)) (fun (y : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p)) => Exists.{succ u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p')) (fun (z : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p')) => Eq.{succ u2} M (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) (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 _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p)) y) (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 _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p')) z)) x)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {x : M} {p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3}, Iff (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (Exists.{succ u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p)) (fun (y : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p)) => Exists.{succ u2} (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p')) (fun (z : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) x p')) => Eq.{succ u2} M (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) (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 _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p)) y) (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 _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p')) z)) x)))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_sup' Submodule.mem_sup'ₓ'. -/
 theorem mem_sup' : x ∈ p ⊔ p' ↔ ∃ (y : p)(z : p'), (y : M) + z = x :=
   mem_sup.trans <| by simp only [SetLike.exists, coe_mk]
@@ -659,9 +659,9 @@ variable (p p')
 
 /- warning: submodule.coe_sup -> Submodule.coe_sup 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (HasSup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (HAdd.hAdd.{u2, u2, u2} (Set.{u2} M) (Set.{u2} M) (Set.{u2} M) (instHAdd.{u2} (Set.{u2} M) (Set.add.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p'))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (HAdd.hAdd.{u2, u2, u2} (Set.{u2} M) (Set.{u2} M) (Set.{u2} M) (instHAdd.{u2} (Set.{u2} M) (Set.add.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} M) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) p'))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (HasSup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (HAdd.hAdd.{u2, u2, u2} (Set.{u2} M) (Set.{u2} M) (Set.{u2} M) (instHAdd.{u2} (Set.{u2} M) (Set.add.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p'))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (HAdd.hAdd.{u2, u2, u2} (Set.{u2} M) (Set.{u2} M) (Set.{u2} M) (instHAdd.{u2} (Set.{u2} M) (Set.add.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) p'))
 Case conversion may be inaccurate. Consider using '#align submodule.coe_sup Submodule.coe_supₓ'. -/
 theorem coe_sup : ↑(p ⊔ p') = (p + p' : Set M) :=
   by
@@ -672,9 +672,9 @@ theorem coe_sup : ↑(p ⊔ p') = (p + p' : Set M) :=
 
 /- warning: submodule.sup_to_add_submonoid -> Submodule.sup_toAddSubmonoid 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (HasSup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (HasSup.sup.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SemilatticeSup.toHasSup.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Lattice.toSemilatticeSup.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (ConditionallyCompleteLattice.toLattice.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (CompleteLattice.toConditionallyCompleteLattice.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (AddSubmonoid.completeLattice.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))))) (Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 p'))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (Sup.sup.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SemilatticeSup.toHasSup.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Lattice.toSemilatticeSup.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (ConditionallyCompleteLattice.toLattice.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (CompleteLattice.toConditionallyCompleteLattice.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (AddSubmonoid.completeLattice.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))))) (Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 p'))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (HasSup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (HasSup.sup.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SemilatticeSup.toHasSup.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Lattice.toSemilatticeSup.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (ConditionallyCompleteLattice.toLattice.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (CompleteLattice.toConditionallyCompleteLattice.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))))) (Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 p'))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), Eq.{succ u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p')) (Sup.sup.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SemilatticeSup.toSup.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Lattice.toSemilatticeSup.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (ConditionallyCompleteLattice.toLattice.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (CompleteLattice.toConditionallyCompleteLattice.{u2} (AddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))))) (Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 p) (Submodule.toAddSubmonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 p'))
 Case conversion may be inaccurate. Consider using '#align submodule.sup_to_add_submonoid Submodule.sup_toAddSubmonoidₓ'. -/
 theorem sup_toAddSubmonoid : (p ⊔ p').toAddSubmonoid = p.toAddSubmonoid ⊔ p'.toAddSubmonoid :=
   by
@@ -685,9 +685,9 @@ theorem sup_toAddSubmonoid : (p ⊔ p').toAddSubmonoid = p.toAddSubmonoid ⊔ p'
 
 /- warning: submodule.sup_to_add_subgroup -> Submodule.sup_toAddSubgroup is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_7 : Ring.{u1} R] [_inst_8 : AddCommGroup.{u2} M] [_inst_9 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9), Eq.{succ u2} (AddSubgroup.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_8)) (Submodule.toAddSubgroup.{u1, u2} R M _inst_7 _inst_8 _inst_9 (HasSup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9))))) p p')) (HasSup.sup.{u2} (AddSubgroup.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_8)) (SemilatticeSup.toHasSup.{u2} (AddSubgroup.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_8)) (Lattice.toSemilatticeSup.{u2} (AddSubgroup.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_8)) (ConditionallyCompleteLattice.toLattice.{u2} (AddSubgroup.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_8)) (CompleteLattice.toConditionallyCompleteLattice.{u2} (AddSubgroup.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_8)) (AddSubgroup.completeLattice.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_8)))))) (Submodule.toAddSubgroup.{u1, u2} R M _inst_7 _inst_8 _inst_9 p) (Submodule.toAddSubgroup.{u1, u2} R M _inst_7 _inst_8 _inst_9 p'))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_7 : Ring.{u1} R] [_inst_8 : AddCommGroup.{u2} M] [_inst_9 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8)] (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (p' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9), Eq.{succ u2} (AddSubgroup.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_8)) (Submodule.toAddSubgroup.{u1, u2} R M _inst_7 _inst_8 _inst_9 (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_7) (AddCommGroup.toAddCommMonoid.{u2} M _inst_8) _inst_9))))) p p')) (Sup.sup.{u2} (AddSubgroup.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_8)) (SemilatticeSup.toHasSup.{u2} (AddSubgroup.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_8)) (Lattice.toSemilatticeSup.{u2} (AddSubgroup.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_8)) (ConditionallyCompleteLattice.toLattice.{u2} (AddSubgroup.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_8)) (CompleteLattice.toConditionallyCompleteLattice.{u2} (AddSubgroup.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_8)) (AddSubgroup.completeLattice.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_8)))))) (Submodule.toAddSubgroup.{u1, u2} R M _inst_7 _inst_8 _inst_9 p) (Submodule.toAddSubgroup.{u1, u2} R M _inst_7 _inst_8 _inst_9 p'))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_7 : Ring.{u2} R] [_inst_8 : AddCommGroup.{u1} M] [_inst_9 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_8)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_8) _inst_9) (p' : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_8) _inst_9), Eq.{succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_8)) (Submodule.toAddSubgroup.{u2, u1} R M _inst_7 _inst_8 _inst_9 (HasSup.sup.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_8) _inst_9) (SemilatticeSup.toHasSup.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_8) _inst_9) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_8) _inst_9) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_8) _inst_9) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_8) _inst_9) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_8) _inst_9))))) p p')) (HasSup.sup.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_8)) (SemilatticeSup.toHasSup.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_8)) (Lattice.toSemilatticeSup.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_8)) (ConditionallyCompleteLattice.toLattice.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_8)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_8)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_8)))))) (Submodule.toAddSubgroup.{u2, u1} R M _inst_7 _inst_8 _inst_9 p) (Submodule.toAddSubgroup.{u2, u1} R M _inst_7 _inst_8 _inst_9 p'))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_7 : Ring.{u2} R] [_inst_8 : AddCommGroup.{u1} M] [_inst_9 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_8)] (p : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_8) _inst_9) (p' : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_8) _inst_9), Eq.{succ u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_8)) (Submodule.toAddSubgroup.{u2, u1} R M _inst_7 _inst_8 _inst_9 (Sup.sup.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_8) _inst_9) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_8) _inst_9) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_8) _inst_9) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_8) _inst_9) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_8) _inst_9) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_7) (AddCommGroup.toAddCommMonoid.{u1} M _inst_8) _inst_9))))) p p')) (Sup.sup.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_8)) (SemilatticeSup.toSup.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_8)) (Lattice.toSemilatticeSup.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_8)) (ConditionallyCompleteLattice.toLattice.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_8)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (AddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_8)) (AddSubgroup.instCompleteLatticeAddSubgroup.{u1} M (AddCommGroup.toAddGroup.{u1} M _inst_8)))))) (Submodule.toAddSubgroup.{u2, u1} R M _inst_7 _inst_8 _inst_9 p) (Submodule.toAddSubgroup.{u2, u1} R M _inst_7 _inst_8 _inst_9 p'))
 Case conversion may be inaccurate. Consider using '#align submodule.sup_to_add_subgroup Submodule.sup_toAddSubgroupₓ'. -/
 theorem sup_toAddSubgroup {R M : Type _} [Ring R] [AddCommGroup M] [Module R M]
     (p p' : Submodule R M) : (p ⊔ p').toAddSubgroup = p.toAddSubgroup ⊔ p'.toAddSubgroup :=
@@ -896,11 +896,15 @@ theorem mem_span_pair {x y z : M} : z ∈ span R ({x, y} : Set M) ↔ ∃ a b :
   simp_rw [mem_span_insert, mem_span_singleton, exists_prop, exists_exists_eq_and, eq_comm]
 #align submodule.mem_span_pair Submodule.mem_span_pair
 
-#print Submodule.span_insert /-
+/- warning: submodule.span_insert -> Submodule.span_insert 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (x : M) (s : Set.{u2} M), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Insert.insert.{u2, u2} M (Set.{u2} M) (Set.hasInsert.{u2} M) x s)) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) x)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (x : M) (s : Set.{u2} M), Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Insert.insert.{u2, u2} M (Set.{u2} M) (Set.instInsertSet.{u2} M) x s)) (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.instSingletonSet.{u2} M) x)) (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 s))
+Case conversion may be inaccurate. Consider using '#align submodule.span_insert Submodule.span_insertₓ'. -/
 theorem span_insert (x) (s : Set M) : span R (insert x s) = span R ({x} : Set M) ⊔ span R s := by
   rw [insert_eq, span_union]
 #align submodule.span_insert Submodule.span_insert
--/
 
 /- warning: submodule.span_insert_eq_span -> Submodule.span_insert_eq_span is a dubious translation:
 lean 3 declaration is
@@ -1248,9 +1252,9 @@ theorem submodule_eq_supₛ_le_nonzero_spans (p : Submodule R M) :
 
 /- warning: submodule.lt_sup_iff_not_mem -> Submodule.lt_sup_iff_not_mem 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] {I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {a : M}, Iff (LT.lt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) I (HasSup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) I (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) a)))) (Not (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) a I))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] {I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3} {a : M}, Iff (LT.lt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) I (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) I (Submodule.span.{u1, u2} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u2, u2} M (Set.{u2} M) (Set.hasSingleton.{u2} M) a)))) (Not (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) a I))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {I : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3} {a : M}, Iff (LT.lt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) I (HasSup.sup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) I (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) a)))) (Not (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) a I))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] {I : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3} {a : M}, Iff (LT.lt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) I (Sup.sup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) I (Submodule.span.{u2, u1} R M _inst_1 _inst_2 _inst_3 (Singleton.singleton.{u1, u1} M (Set.{u1} M) (Set.instSingletonSet.{u1} M) a)))) (Not (Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.instSetLikeSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_3)) a I))
 Case conversion may be inaccurate. Consider using '#align submodule.lt_sup_iff_not_mem Submodule.lt_sup_iff_not_memₓ'. -/
 theorem lt_sup_iff_not_mem {I : Submodule R M} {a : M} : (I < I ⊔ R ∙ a) ↔ a ∉ I :=
   by
@@ -1408,9 +1412,9 @@ theorem prod_mono {p p' : Submodule R M} {q q' : Submodule R M'} :
 
 /- warning: submodule.prod_inf_prod -> Submodule.prod_inf_prod 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {M' : Type.{u3}} [_inst_7 : AddCommMonoid.{u3} M'] [_inst_8 : Module.{u1, u3} R M' _inst_1 _inst_7] (q₁ : Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (q₁' : Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8), Eq.{succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (HasInf.inf.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Submodule.hasInf.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 p M' _inst_7 _inst_8 q₁) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 p' M' _inst_7 _inst_8 q₁')) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 (HasInf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_2 _inst_3) p p') M' _inst_7 _inst_8 (HasInf.inf.{u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (Submodule.hasInf.{u1, u3} R M' _inst_1 _inst_7 _inst_8) q₁ q₁'))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {M' : Type.{u3}} [_inst_7 : AddCommMonoid.{u3} M'] [_inst_8 : Module.{u1, u3} R M' _inst_1 _inst_7] (q₁ : Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (q₁' : Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8), Eq.{succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Inf.inf.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Submodule.hasInf.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 p M' _inst_7 _inst_8 q₁) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 p' M' _inst_7 _inst_8 q₁')) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 (Inf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_2 _inst_3) p p') M' _inst_7 _inst_8 (Inf.inf.{u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (Submodule.hasInf.{u1, u3} R M' _inst_1 _inst_7 _inst_8) q₁ q₁'))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] (p : Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) {M' : Type.{u2}} [_inst_7 : AddCommMonoid.{u2} M'] [_inst_8 : Module.{u1, u2} R M' _inst_1 _inst_7] (q₁ : Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) (q₁' : Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (HasInf.inf.{max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Submodule.instHasInfSubmodule.{u1, max u3 u2} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Submodule.prod.{u1, u3, u2} R M _inst_1 _inst_2 _inst_3 p M' _inst_7 _inst_8 q₁) (Submodule.prod.{u1, u3, u2} R M _inst_1 _inst_2 _inst_3 p' M' _inst_7 _inst_8 q₁')) (Submodule.prod.{u1, u3, u2} R M _inst_1 _inst_2 _inst_3 (HasInf.inf.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.instHasInfSubmodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) p p') M' _inst_7 _inst_8 (HasInf.inf.{u2} (Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) (Submodule.instHasInfSubmodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) q₁ q₁'))
+  forall {R : Type.{u1}} {M : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] (p : Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) {M' : Type.{u2}} [_inst_7 : AddCommMonoid.{u2} M'] [_inst_8 : Module.{u1, u2} R M' _inst_1 _inst_7] (q₁ : Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) (q₁' : Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Inf.inf.{max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Submodule.instInfSubmodule.{u1, max u3 u2} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Submodule.prod.{u1, u3, u2} R M _inst_1 _inst_2 _inst_3 p M' _inst_7 _inst_8 q₁) (Submodule.prod.{u1, u3, u2} R M _inst_1 _inst_2 _inst_3 p' M' _inst_7 _inst_8 q₁')) (Submodule.prod.{u1, u3, u2} R M _inst_1 _inst_2 _inst_3 (Inf.inf.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.instInfSubmodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) p p') M' _inst_7 _inst_8 (Inf.inf.{u2} (Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) (Submodule.instInfSubmodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) q₁ q₁'))
 Case conversion may be inaccurate. Consider using '#align submodule.prod_inf_prod Submodule.prod_inf_prodₓ'. -/
 @[simp]
 theorem prod_inf_prod : prod p q₁ ⊓ prod p' q₁' = prod (p ⊓ p') (q₁ ⊓ q₁') :=
@@ -1419,9 +1423,9 @@ theorem prod_inf_prod : prod p q₁ ⊓ prod p' q₁' = prod (p ⊓ p') (q₁ 
 
 /- warning: submodule.prod_sup_prod -> Submodule.prod_sup_prod 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_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {M' : Type.{u3}} [_inst_7 : AddCommMonoid.{u3} M'] [_inst_8 : Module.{u1, u3} R M' _inst_1 _inst_7] (q₁ : Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (q₁' : Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8), Eq.{succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (HasSup.sup.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (SemilatticeSup.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Lattice.toSemilatticeSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (ConditionallyCompleteLattice.toLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)))))) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 p M' _inst_7 _inst_8 q₁) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 p' M' _inst_7 _inst_8 q₁')) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 (HasSup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p') M' _inst_7 _inst_8 (HasSup.sup.{u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (SemilatticeSup.toHasSup.{u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (Lattice.toSemilatticeSup.{u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (ConditionallyCompleteLattice.toLattice.{u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (Submodule.completeLattice.{u1, u3} R M' _inst_1 _inst_7 _inst_8))))) q₁ q₁'))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (p : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) {M' : Type.{u3}} [_inst_7 : AddCommMonoid.{u3} M'] [_inst_8 : Module.{u1, u3} R M' _inst_1 _inst_7] (q₁ : Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (q₁' : Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8), Eq.{succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Sup.sup.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (SemilatticeSup.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Lattice.toSemilatticeSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (ConditionallyCompleteLattice.toLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Submodule.completeLattice.{u1, max u2 u3} R (Prod.{u2, u3} M M') _inst_1 (Prod.addCommMonoid.{u2, u3} M M' _inst_2 _inst_7) (Prod.module.{u1, u2, u3} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)))))) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 p M' _inst_7 _inst_8 q₁) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 p' M' _inst_7 _inst_8 q₁')) (Submodule.prod.{u1, u2, u3} R M _inst_1 _inst_2 _inst_3 (Sup.sup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) p p') M' _inst_7 _inst_8 (Sup.sup.{u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (SemilatticeSup.toHasSup.{u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (Lattice.toSemilatticeSup.{u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (ConditionallyCompleteLattice.toLattice.{u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u1, u3} R M' _inst_1 _inst_7 _inst_8) (Submodule.completeLattice.{u1, u3} R M' _inst_1 _inst_7 _inst_8))))) q₁ q₁'))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] (p : Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) {M' : Type.{u2}} [_inst_7 : AddCommMonoid.{u2} M'] [_inst_8 : Module.{u1, u2} R M' _inst_1 _inst_7] (q₁ : Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) (q₁' : Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (HasSup.sup.{max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (SemilatticeSup.toHasSup.{max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Lattice.toSemilatticeSup.{max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (ConditionallyCompleteLattice.toLattice.{max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Submodule.completeLattice.{u1, max u3 u2} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)))))) (Submodule.prod.{u1, u3, u2} R M _inst_1 _inst_2 _inst_3 p M' _inst_7 _inst_8 q₁) (Submodule.prod.{u1, u3, u2} R M _inst_1 _inst_2 _inst_3 p' M' _inst_7 _inst_8 q₁')) (Submodule.prod.{u1, u3, u2} R M _inst_1 _inst_2 _inst_3 (HasSup.sup.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u3} R M _inst_1 _inst_2 _inst_3))))) p p') M' _inst_7 _inst_8 (HasSup.sup.{u2} (Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) (Submodule.completeLattice.{u1, u2} R M' _inst_1 _inst_7 _inst_8))))) q₁ q₁'))
+  forall {R : Type.{u1}} {M : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u1, u3} R M _inst_1 _inst_2] (p : Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (p' : Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) {M' : Type.{u2}} [_inst_7 : AddCommMonoid.{u2} M'] [_inst_8 : Module.{u1, u2} R M' _inst_1 _inst_7] (q₁ : Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) (q₁' : Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8), Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Sup.sup.{max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (SemilatticeSup.toSup.{max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Lattice.toSemilatticeSup.{max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (ConditionallyCompleteLattice.toLattice.{max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u2 u3} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)) (Submodule.completeLattice.{u1, max u3 u2} R (Prod.{u3, u2} M M') _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} M M' _inst_2 _inst_7) (Prod.module.{u1, u3, u2} R M M' _inst_1 _inst_2 _inst_7 _inst_3 _inst_8)))))) (Submodule.prod.{u1, u3, u2} R M _inst_1 _inst_2 _inst_3 p M' _inst_7 _inst_8 q₁) (Submodule.prod.{u1, u3, u2} R M _inst_1 _inst_2 _inst_3 p' M' _inst_7 _inst_8 q₁')) (Submodule.prod.{u1, u3, u2} R M _inst_1 _inst_2 _inst_3 (Sup.sup.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u1, u3} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u3} R M _inst_1 _inst_2 _inst_3))))) p p') M' _inst_7 _inst_8 (Sup.sup.{u2} (Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M' _inst_1 _inst_7 _inst_8) (Submodule.completeLattice.{u1, u2} R M' _inst_1 _inst_7 _inst_8))))) q₁ q₁'))
 Case conversion may be inaccurate. Consider using '#align submodule.prod_sup_prod Submodule.prod_sup_prodₓ'. -/
 @[simp]
 theorem prod_sup_prod : prod p q₁ ⊔ prod p' q₁' = prod (p ⊔ p') (q₁ ⊔ q₁') :=
@@ -1496,9 +1500,9 @@ include sc
 
 /- warning: submodule.comap_map_eq -> Submodule.comap_map_eq is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u5}} [sc : SemilinearMapClass.{u5, u1, u2, u3, u4} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_4 _inst_6] (f : F) (p : Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4), Eq.{succ u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (Submodule.comap.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ F sc f (Submodule.map.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ _inst_7 F sc f p)) (HasSup.sup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (SemilatticeSup.toHasSup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4))))) p (LinearMap.ker.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ F sc f))
+  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : Module.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] [_inst_5 : AddCommGroup.{u4} M₂] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5)] {τ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u5}} [sc : SemilinearMapClass.{u5, u1, u2, u3, u4} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_4 _inst_6] (f : F) (p : Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4), Eq.{succ u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (Submodule.comap.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ F sc f (Submodule.map.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ _inst_7 F sc f p)) (Sup.sup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (SemilatticeSup.toHasSup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4))))) p (LinearMap.ker.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ F sc f))
 but is expected to have type
-  forall {R : Type.{u5}} {R₂ : Type.{u3}} {M : Type.{u4}} {M₂ : Type.{u2}} [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u3} R₂] [_inst_3 : AddCommGroup.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3)] [_inst_5 : AddCommGroup.{u2} M₂] [_inst_6 : Module.{u3, u2} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_5)] {τ₁₂ : RingHom.{u5, u3} R R₂ (Semiring.toNonAssocSemiring.{u5} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u5, u3} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u1}} [sc : SemilinearMapClass.{u1, u5, u3, u4, u2} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_5) _inst_4 _inst_6] (f : F) (p : Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4), Eq.{succ u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) (Submodule.comap.{u5, u3, u4, u2, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ F sc f (Submodule.map.{u5, u3, u4, u2, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ _inst_7 F sc f p)) (HasSup.sup.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) (SemilatticeSup.toHasSup.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) (Submodule.completeLattice.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4))))) p (LinearMap.ker.{u5, u3, u4, u2, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ F sc f))
+  forall {R : Type.{u5}} {R₂ : Type.{u3}} {M : Type.{u4}} {M₂ : Type.{u2}} [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u3} R₂] [_inst_3 : AddCommGroup.{u4} M] [_inst_4 : Module.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3)] [_inst_5 : AddCommGroup.{u2} M₂] [_inst_6 : Module.{u3, u2} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_5)] {τ₁₂ : RingHom.{u5, u3} R R₂ (Semiring.toNonAssocSemiring.{u5} R _inst_1) (Semiring.toNonAssocSemiring.{u3} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u5, u3} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u1}} [sc : SemilinearMapClass.{u1, u5, u3, u4, u2} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_5) _inst_4 _inst_6] (f : F) (p : Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4), Eq.{succ u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) (Submodule.comap.{u5, u3, u4, u2, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ F sc f (Submodule.map.{u5, u3, u4, u2, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ _inst_7 F sc f p)) (Sup.sup.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) (SemilatticeSup.toSup.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) (Submodule.completeLattice.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4))))) p (LinearMap.ker.{u5, u3, u4, u2, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M₂ _inst_5) _inst_4 _inst_6 τ₁₂ F sc f))
 Case conversion may be inaccurate. Consider using '#align submodule.comap_map_eq Submodule.comap_map_eqₓ'. -/
 theorem comap_map_eq (f : F) (p : Submodule R M) : comap f (map f p) = p ⊔ LinearMap.ker f :=
   by
@@ -1545,9 +1549,9 @@ include sc
 
 /- warning: linear_map.map_le_map_iff -> LinearMap.map_le_map_iff is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : AddCommGroup.{u4} M₂] [_inst_5 : Module.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4)] {τ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u5}} [sc : SemilinearMapClass.{u5, u1, u2, u3, u4} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6] (f : F) {p : Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5} {p' : Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5}, Iff (LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (Preorder.toLE.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6)))) (Submodule.map.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p) (Submodule.map.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p')) (LE.le.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Preorder.toLE.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) M (Submodule.setLike.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5)))) p (HasSup.sup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (SemilatticeSup.toHasSup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Lattice.toSemilatticeSup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (ConditionallyCompleteLattice.toLattice.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Submodule.completeLattice.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5))))) p' (LinearMap.ker.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ F sc f)))
+  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : AddCommGroup.{u4} M₂] [_inst_5 : Module.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4)] {τ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u5}} [sc : SemilinearMapClass.{u5, u1, u2, u3, u4} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6] (f : F) {p : Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5} {p' : Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5}, Iff (LE.le.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (Preorder.toLE.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (PartialOrder.toPreorder.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (SetLike.partialOrder.{u4, u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) M₂ (Submodule.setLike.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6)))) (Submodule.map.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p) (Submodule.map.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p')) (LE.le.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Preorder.toLE.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (PartialOrder.toPreorder.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (SetLike.partialOrder.{u3, u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) M (Submodule.setLike.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5)))) p (Sup.sup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (SemilatticeSup.toHasSup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Lattice.toSemilatticeSup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (ConditionallyCompleteLattice.toLattice.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Submodule.completeLattice.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5))))) p' (LinearMap.ker.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ F sc f)))
 but is expected to have type
-  forall {R : Type.{u5}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u3}} [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : AddCommGroup.{u4} M] [_inst_4 : AddCommGroup.{u3} M₂] [_inst_5 : Module.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3)] [_inst_6 : Module.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4)] {τ₁₂ : RingHom.{u5, u2} R R₂ (Semiring.toNonAssocSemiring.{u5} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u5, u2} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u1}} [sc : SemilinearMapClass.{u1, u5, u2, u4, u3} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5 _inst_6] (f : F) {p : Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5} {p' : Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5}, Iff (LE.le.{u3} (Submodule.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_6) (Preorder.toLE.{u3} (Submodule.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_6) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_6) (Submodule.completeLattice.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_6))))) (Submodule.map.{u5, u2, u4, u3, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p) (Submodule.map.{u5, u2, u4, u3, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p')) (LE.le.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (Preorder.toLE.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (PartialOrder.toPreorder.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (Submodule.completeLattice.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5))))) p (HasSup.sup.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (SemilatticeSup.toHasSup.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (Lattice.toSemilatticeSup.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (ConditionallyCompleteLattice.toLattice.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (Submodule.completeLattice.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5))))) p' (LinearMap.ker.{u5, u2, u4, u3, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ F sc f)))
+  forall {R : Type.{u5}} {R₂ : Type.{u2}} {M : Type.{u4}} {M₂ : Type.{u3}} [_inst_1 : Semiring.{u5} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : AddCommGroup.{u4} M] [_inst_4 : AddCommGroup.{u3} M₂] [_inst_5 : Module.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3)] [_inst_6 : Module.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4)] {τ₁₂ : RingHom.{u5, u2} R R₂ (Semiring.toNonAssocSemiring.{u5} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u5, u2} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u1}} [sc : SemilinearMapClass.{u1, u5, u2, u4, u3} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5 _inst_6] (f : F) {p : Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5} {p' : Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5}, Iff (LE.le.{u3} (Submodule.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_6) (Preorder.toLE.{u3} (Submodule.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_6) (PartialOrder.toPreorder.{u3} (Submodule.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submodule.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submodule.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_6) (Submodule.completeLattice.{u2, u3} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_6))))) (Submodule.map.{u5, u2, u4, u3, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p) (Submodule.map.{u5, u2, u4, u3, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p')) (LE.le.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (Preorder.toLE.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (PartialOrder.toPreorder.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (Submodule.completeLattice.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5))))) p (Sup.sup.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (SemilatticeSup.toSup.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (Lattice.toSemilatticeSup.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (ConditionallyCompleteLattice.toLattice.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u4} (Submodule.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5) (Submodule.completeLattice.{u5, u4} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_5))))) p' (LinearMap.ker.{u5, u2, u4, u3, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ F sc f)))
 Case conversion may be inaccurate. Consider using '#align linear_map.map_le_map_iff LinearMap.map_le_map_iffₓ'. -/
 protected theorem map_le_map_iff (f : F) {p p'} : map f p ≤ map f p' ↔ p ≤ p' ⊔ ker f := by
   rw [map_le_iff_le_comap, Submodule.comap_map_eq]
@@ -1575,9 +1579,9 @@ theorem map_injective {f : F} (hf : ker f = ⊥) : Injective (map f) := fun p p'
 
 /- warning: linear_map.map_eq_top_iff -> LinearMap.map_eq_top_iff is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : AddCommGroup.{u4} M₂] [_inst_5 : Module.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4)] {τ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u5}} [sc : SemilinearMapClass.{u5, u1, u2, u3, u4} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6] {f : F}, (Eq.{succ u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (LinearMap.range.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ F sc _inst_7 f) (Top.top.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (Submodule.hasTop.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6))) -> (forall {p : Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5}, Iff (Eq.{succ u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (Submodule.map.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p) (Top.top.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (Submodule.hasTop.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6))) (Eq.{succ u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (HasSup.sup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (SemilatticeSup.toHasSup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Lattice.toSemilatticeSup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (ConditionallyCompleteLattice.toLattice.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Submodule.completeLattice.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5))))) p (LinearMap.ker.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ F sc f)) (Top.top.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Submodule.hasTop.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5))))
+  forall {R : Type.{u1}} {R₂ : Type.{u2}} {M : Type.{u3}} {M₂ : Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} R₂] [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : AddCommGroup.{u4} M₂] [_inst_5 : Module.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] [_inst_6 : Module.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4)] {τ₁₂ : RingHom.{u1, u2} R R₂ (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u2} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u1, u2} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u5}} [sc : SemilinearMapClass.{u5, u1, u2, u3, u4} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6] {f : F}, (Eq.{succ u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (LinearMap.range.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ F sc _inst_7 f) (Top.top.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (Submodule.hasTop.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6))) -> (forall {p : Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5}, Iff (Eq.{succ u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (Submodule.map.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p) (Top.top.{u4} (Submodule.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6) (Submodule.hasTop.{u2, u4} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_6))) (Eq.{succ u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Sup.sup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (SemilatticeSup.toHasSup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Lattice.toSemilatticeSup.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (ConditionallyCompleteLattice.toLattice.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Submodule.completeLattice.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5))))) p (LinearMap.ker.{u1, u2, u3, u4, u5} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) (AddCommGroup.toAddCommMonoid.{u4} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ F sc f)) (Top.top.{u3} (Submodule.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5) (Submodule.hasTop.{u1, u3} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_5))))
 but is expected to have type
-  forall {R : Type.{u3}} {R₂ : Type.{u4}} {M : Type.{u2}} {M₂ : Type.{u5}} [_inst_1 : Semiring.{u3} R] [_inst_2 : Semiring.{u4} R₂] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : AddCommGroup.{u5} M₂] [_inst_5 : Module.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_6 : Module.{u4, u5} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4)] {τ₁₂ : RingHom.{u3, u4} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u4} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u3, u4} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u1}} [sc : SemilinearMapClass.{u1, u3, u4, u2, u5} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_5 _inst_6] {f : F}, (Eq.{succ u5} (Submodule.{u4, u5} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_6) (LinearMap.range.{u3, u4, u2, u5, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ F sc _inst_7 f) (Top.top.{u5} (Submodule.{u4, u5} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_6) (Submodule.instTopSubmodule.{u4, u5} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_6))) -> (forall {p : Submodule.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5}, Iff (Eq.{succ u5} (Submodule.{u4, u5} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_6) (Submodule.map.{u3, u4, u2, u5, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p) (Top.top.{u5} (Submodule.{u4, u5} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_6) (Submodule.instTopSubmodule.{u4, u5} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_6))) (Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5) (HasSup.sup.{u2} (Submodule.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5) (SemilatticeSup.toHasSup.{u2} (Submodule.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5) (Lattice.toSemilatticeSup.{u2} (Submodule.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5) (Submodule.completeLattice.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5))))) p (LinearMap.ker.{u3, u4, u2, u5, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ F sc f)) (Top.top.{u2} (Submodule.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5) (Submodule.instTopSubmodule.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5))))
+  forall {R : Type.{u3}} {R₂ : Type.{u4}} {M : Type.{u2}} {M₂ : Type.{u5}} [_inst_1 : Semiring.{u3} R] [_inst_2 : Semiring.{u4} R₂] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : AddCommGroup.{u5} M₂] [_inst_5 : Module.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_6 : Module.{u4, u5} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4)] {τ₁₂ : RingHom.{u3, u4} R R₂ (Semiring.toNonAssocSemiring.{u3} R _inst_1) (Semiring.toNonAssocSemiring.{u4} R₂ _inst_2)} [_inst_7 : RingHomSurjective.{u3, u4} R R₂ _inst_1 _inst_2 τ₁₂] {F : Type.{u1}} [sc : SemilinearMapClass.{u1, u3, u4, u2, u5} F R R₂ _inst_1 _inst_2 τ₁₂ M M₂ (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_5 _inst_6] {f : F}, (Eq.{succ u5} (Submodule.{u4, u5} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_6) (LinearMap.range.{u3, u4, u2, u5, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ F sc _inst_7 f) (Top.top.{u5} (Submodule.{u4, u5} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_6) (Submodule.instTopSubmodule.{u4, u5} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_6))) -> (forall {p : Submodule.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5}, Iff (Eq.{succ u5} (Submodule.{u4, u5} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_6) (Submodule.map.{u3, u4, u2, u5, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ _inst_7 F sc f p) (Top.top.{u5} (Submodule.{u4, u5} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_6) (Submodule.instTopSubmodule.{u4, u5} R₂ M₂ _inst_2 (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_6))) (Eq.{succ u2} (Submodule.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5) (Sup.sup.{u2} (Submodule.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5) (SemilatticeSup.toSup.{u2} (Submodule.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5) (Lattice.toSemilatticeSup.{u2} (Submodule.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5) (Submodule.completeLattice.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5))))) p (LinearMap.ker.{u3, u4, u2, u5, u1} R R₂ M M₂ _inst_1 _inst_2 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u5} M₂ _inst_4) _inst_5 _inst_6 τ₁₂ F sc f)) (Top.top.{u2} (Submodule.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5) (Submodule.instTopSubmodule.{u3, u2} R M _inst_1 (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_5))))
 Case conversion may be inaccurate. Consider using '#align linear_map.map_eq_top_iff LinearMap.map_eq_top_iffₓ'. -/
 theorem map_eq_top_iff {f : F} (hf : range f = ⊤) {p : Submodule R M} :
     p.map f = ⊤ ↔ p ⊔ LinearMap.ker f = ⊤ := by
@@ -1711,9 +1715,9 @@ open Classical
 
 /- warning: linear_map.span_singleton_sup_ker_eq_top -> LinearMap.span_singleton_sup_ker_eq_top is a dubious translation:
 lean 3 declaration is
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (f : LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) {x : V}, (Ne.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) => V -> K) (LinearMap.hasCoeToFun.{u1, u1, u2, u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f x) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (HasSup.sup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)) (LinearMap.ker.{u1, u1, u2, u1, max u2 u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.semilinearMapClass.{u1, u1, u2, u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f)) (Top.top.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Field.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (f : LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) {x : V}, (Ne.{succ u1} K (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (fun (_x : LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) => V -> K) (LinearMap.hasCoeToFun.{u1, u1, u2, u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f x) (OfNat.ofNat.{u1} K 0 (OfNat.mk.{u1} K 0 (Zero.zero.{u1} K (MulZeroClass.toHasZero.{u1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))))))))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Sup.sup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) x)) (LinearMap.ker.{u1, u1, u2, u1, max u2 u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))))) (LinearMap.semilinearMapClass.{u1, u1, u2, u1} K K V K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) _inst_3 (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1)))))) f)) (Top.top.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))
 but is expected to have type
-  forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] (f : LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1)) {x : V}, (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1)) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) (CommGroupWithZero.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) (Semifield.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) _inst_1))))))) -> (Eq.{succ u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (HasSup.sup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Submodule.span.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3 (Singleton.singleton.{u1, u1} V (Set.{u1} V) (Set.instSingletonSet.{u1} V) x)) (LinearMap.ker.{u2, u2, u1, u2, max u2 u1} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f)) (Top.top.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3)))
+  forall {K : Type.{u2}} {V : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] (f : LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1)) {x : V}, (Ne.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1)) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f x) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) (CommGroupWithZero.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) (Semifield.toCommGroupWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) (Field.toSemifield.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : V) => K) x) _inst_1))))))) -> (Eq.{succ u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Sup.sup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) (Submodule.span.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3 (Singleton.singleton.{u1, u1} V (Set.{u1} V) (Set.instSingletonSet.{u1} V) x)) (LinearMap.ker.{u2, u2, u1, u2, max u2 u1} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) (LinearMap.{u2, u2, u1, u2} K K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))))) V K (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u2} K K V K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonUnitalRing.toNonUnitalNonAssocRing.{u2} K (NonUnitalCommRing.toNonUnitalRing.{u2} K (CommRing.toNonUnitalCommRing.{u2} K (Field.toCommRing.{u2} K _inst_1)))))) _inst_3 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRing.{u2} K _inst_1) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)))))) f)) (Top.top.{u1} (Submodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} K V (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3)))
 Case conversion may be inaccurate. Consider using '#align linear_map.span_singleton_sup_ker_eq_top LinearMap.span_singleton_sup_ker_eq_topₓ'. -/
 theorem span_singleton_sup_ker_eq_top (f : V →ₗ[K] K) {x : V} (hx : f x ≠ 0) :
     (K ∙ x) ⊔ f.ker = ⊤ :=

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

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

@@ -335,7 +335,7 @@ theorem span_eq_iSup_of_singleton_spans (s : Set M) : span R s = ⨆ x ∈ s, R
   simp only [← span_iUnion, Set.biUnion_of_singleton s]
 #align submodule.span_eq_supr_of_singleton_spans Submodule.span_eq_iSup_of_singleton_spans
 
-theorem span_range_eq_iSup {ι : Type*} {v : ι → M} : span R (range v) = ⨆ i, R ∙ v i := by
+theorem span_range_eq_iSup {ι : Sort*} {v : ι → M} : span R (range v) = ⨆ i, R ∙ v i := by
   rw [span_eq_iSup_of_singleton_spans, iSup_range]
 #align submodule.span_range_eq_supr Submodule.span_range_eq_iSup
 
@@ -1097,7 +1097,7 @@ theorem ext_on {s : Set M} {f g : F} (hv : span R s = ⊤) (h : Set.EqOn f g s)
 
 /-- If the range of `v : ι → M` generates the whole module and linear maps `f`, `g` are equal at
 each `v i`, then they are equal. -/
-theorem ext_on_range {ι : Type*} {v : ι → M} {f g : F} (hv : span R (Set.range v) = ⊤)
+theorem ext_on_range {ι : Sort*} {v : ι → M} {f g : F} (hv : span R (Set.range v) = ⊤)
     (h : ∀ i, f (v i) = g (v i)) : f = g :=
   ext_on hv (Set.forall_mem_range.2 h)
 #align linear_map.ext_on_range LinearMap.ext_on_range

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -1029,7 +1029,7 @@ def toSpanSingleton (x : M) : R →ₗ[R] M :=
   LinearMap.id.smulRight x
 #align linear_map.to_span_singleton LinearMap.toSpanSingleton
 
-/-- The range of `toSpanSingleton x` is the span of `x`.-/
+/-- The range of `toSpanSingleton x` is the span of `x`. -/
 theorem span_singleton_eq_range (x : M) : (R ∙ x) = range (toSpanSingleton R M x) :=
   Submodule.ext fun y => by
     refine' Iff.trans _ LinearMap.mem_range.symm

Quoting [@digama0](https://github.com/digama0):

These were actually never meant to go in the file, they are basically debugging information and only useful on significantly broken mathport files. You can safely remove all of them.

@@ -326,7 +326,6 @@ theorem sup_span : p ⊔ span R s = span R (p ∪ s) := by rw [Submodule.span_un
 theorem span_sup : span R s ⊔ p = span R (s ∪ p) := by rw [Submodule.span_union, p.span_eq]
 #align submodule.span_sup Submodule.span_sup
 
--- mathport name: «expr ∙ »
 notation:1000
   /- Note that the character `∙` U+2219 used below is different from the scalar multiplication
 character `•` U+2022. -/

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

| Statement | New name | Old name | |

@@ -885,7 +885,7 @@ instance : IsModularLattice (Submodule R M) :=
     rcases ha with ⟨⟨b, hb, c, hc, rfl⟩, haz⟩
     rw [mem_sup]
     refine' ⟨b, hb, c, mem_inf.2 ⟨hc, _⟩, rfl⟩
-    rw [← add_sub_cancel c b, add_comm]
+    rw [← add_sub_cancel_right c b, add_comm]
     apply z.sub_mem haz (xz hb)⟩
 
 end AddCommGroup

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)

@@ -36,11 +36,8 @@ open Pointwise
 section AddCommMonoid
 
 variable [Semiring R] [AddCommMonoid M] [Module R M]
-
 variable {x : M} (p p' : Submodule R M)
-
 variable [Semiring R₂] {σ₁₂ : R →+* R₂}
-
 variable [AddCommMonoid M₂] [Module R₂ M₂]
 variable {F : Type*} [FunLike F M M₂] [SemilinearMapClass F σ₁₂ M M₂]
 
@@ -896,11 +893,8 @@ end AddCommGroup
 section AddCommGroup
 
 variable [Semiring R] [Semiring R₂]
-
 variable [AddCommGroup M] [Module R M] [AddCommGroup M₂] [Module R₂ M₂]
-
 variable {τ₁₂ : R →+* R₂} [RingHomSurjective τ₁₂]
-
 variable {F : Type*} [FunLike F M M₂] [SemilinearMapClass F τ₁₂ M M₂]
 
 theorem comap_map_eq (f : F) (p : Submodule R M) : comap f (map f p) = p ⊔ LinearMap.ker f := by
@@ -1001,13 +995,9 @@ open Submodule Function
 section AddCommGroup
 
 variable [Semiring R] [Semiring R₂]
-
 variable [AddCommGroup M] [AddCommGroup M₂]
-
 variable [Module R M] [Module R₂ M₂]
-
 variable {τ₁₂ : R →+* R₂} [RingHomSurjective τ₁₂]
-
 variable {F : Type*} [FunLike F M M₂] [SemilinearMapClass F τ₁₂ M M₂]
 
 protected theorem map_le_map_iff (f : F) {p p'} : map f p ≤ map f p' ↔ p ≤ p' ⊔ ker f := by
@@ -1076,9 +1066,7 @@ end
 section AddCommMonoid
 
 variable [Semiring R] [AddCommMonoid M] [Module R M]
-
 variable [Semiring R₂] [AddCommMonoid M₂] [Module R₂ M₂]
-
 variable {F : Type*} {σ₁₂ : R →+* R₂} [FunLike F M M₂] [SemilinearMapClass F σ₁₂ M M₂]
 
 /-- Two linear maps are equal on `Submodule.span s` iff they are equal on `s`. -/

These are the case names used by the induction tactic after the with.

This replaces H0, H1, Hmul etc with zero, one, mul.

This PR does not touch Submonoid or Subgroup, as to_additive does not know how to rename the argument names. There are ways to work around this, but I'd prefer to leave them to a later PR.

This also leaves the closure_induction₂ variants alone, as renaming the arguments is more work for less gain.

@@ -167,40 +167,40 @@ theorem span_closure {s : Set M} : span R (AddSubmonoid.closure s : Set M) = spa
 preserved under addition and scalar multiplication, then `p` holds for all elements of the span of
 `s`. -/
 @[elab_as_elim]
-theorem span_induction {p : M → Prop} (h : x ∈ span R s) (Hs : ∀ x ∈ s, p x) (H0 : p 0)
-    (H1 : ∀ x y, p x → p y → p (x + y)) (H2 : ∀ (a : R) (x), p x → p (a • x)) : p x :=
-  ((@span_le (p := ⟨⟨⟨p, by intros x y; exact H1 x y⟩, H0⟩, H2⟩)) s).2 Hs h
+theorem span_induction {p : M → Prop} (h : x ∈ span R s) (mem : ∀ x ∈ s, p x) (zero : p 0)
+    (add : ∀ x y, p x → p y → p (x + y)) (smul : ∀ (a : R) (x), p x → p (a • x)) : p x :=
+  ((@span_le (p := ⟨⟨⟨p, by intros x y; exact add x y⟩, zero⟩, smul⟩)) s).2 mem h
 #align submodule.span_induction Submodule.span_induction
 
 /-- An induction principle for span membership. This is a version of `Submodule.span_induction`
 for binary predicates. -/
 theorem span_induction₂ {p : M → M → Prop} {a b : M} (ha : a ∈ Submodule.span R s)
-    (hb : b ∈ Submodule.span R s) (Hs : ∀ x ∈ s, ∀ y ∈ s, p x y)
-    (H0_left : ∀ y, p 0 y) (H0_right : ∀ x, p x 0)
-    (Hadd_left : ∀ x₁ x₂ y, p x₁ y → p x₂ y → p (x₁ + x₂) y)
-    (Hadd_right : ∀ x y₁ y₂, p x y₁ → p x y₂ → p x (y₁ + y₂))
-    (Hsmul_left : ∀ (r : R) x y, p x y → p (r • x) y)
-    (Hsmul_right : ∀ (r : R) x y, p x y → p x (r • y)) : p a b :=
+    (hb : b ∈ Submodule.span R s) (mem_mem : ∀ x ∈ s, ∀ y ∈ s, p x y)
+    (zero_left : ∀ y, p 0 y) (zero_right : ∀ x, p x 0)
+    (add_left : ∀ x₁ x₂ y, p x₁ y → p x₂ y → p (x₁ + x₂) y)
+    (add_right : ∀ x y₁ y₂, p x y₁ → p x y₂ → p x (y₁ + y₂))
+    (smul_left : ∀ (r : R) x y, p x y → p (r • x) y)
+    (smul_right : ∀ (r : R) x y, p x y → p x (r • y)) : p a b :=
   Submodule.span_induction ha
-    (fun x hx => Submodule.span_induction hb (Hs x hx) (H0_right x) (Hadd_right x) fun r =>
-      Hsmul_right r x)
-    (H0_left b) (fun x₁ x₂ => Hadd_left x₁ x₂ b) fun r x => Hsmul_left r x b
+    (fun x hx => Submodule.span_induction hb (mem_mem x hx) (zero_right x) (add_right x) fun r =>
+      smul_right r x)
+    (zero_left b) (fun x₁ x₂ => add_left x₁ x₂ b) fun r x => smul_left r x b
 
 /-- A dependent version of `Submodule.span_induction`. -/
 @[elab_as_elim]
 theorem span_induction' {p : ∀ x, x ∈ span R s → Prop}
-    (Hs : ∀ (x) (h : x ∈ s), p x (subset_span h))
-    (H0 : p 0 (Submodule.zero_mem _))
-    (H1 : ∀ x hx y hy, p x hx → p y hy → p (x + y) (Submodule.add_mem _ ‹_› ‹_›))
-    (H2 : ∀ (a : R) (x hx), p x hx → p (a • x) (Submodule.smul_mem _ _ ‹_›)) {x}
+    (mem : ∀ (x) (h : x ∈ s), p x (subset_span h))
+    (zero : p 0 (Submodule.zero_mem _))
+    (add : ∀ x hx y hy, p x hx → p y hy → p (x + y) (Submodule.add_mem _ ‹_› ‹_›))
+    (smul : ∀ (a : R) (x hx), p x hx → p (a • x) (Submodule.smul_mem _ _ ‹_›)) {x}
     (hx : x ∈ span R s) : p x hx := by
   refine' Exists.elim _ fun (hx : x ∈ span R s) (hc : p x hx) => hc
   refine'
-    span_induction hx (fun m hm => ⟨subset_span hm, Hs m hm⟩) ⟨zero_mem _, H0⟩
+    span_induction hx (fun m hm => ⟨subset_span hm, mem m hm⟩) ⟨zero_mem _, zero⟩
       (fun x y hx hy =>
         Exists.elim hx fun hx' hx =>
-          Exists.elim hy fun hy' hy => ⟨add_mem hx' hy', H1 _ _ _ _ hx hy⟩)
-      fun r x hx => Exists.elim hx fun hx' hx => ⟨smul_mem _ _ hx', H2 r _ _ hx⟩
+          Exists.elim hy fun hy' hy => ⟨add_mem hx' hy', add _ _ _ _ hx hy⟩)
+      fun r x hx => Exists.elim hx fun hx' hx => ⟨smul_mem _ _ hx', smul r _ _ hx⟩
 #align submodule.span_induction' Submodule.span_induction'
 
 open AddSubmonoid in
@@ -217,25 +217,25 @@ theorem span_eq_closure {s : Set M} : (span R s).toAddSubmonoid = closure (@univ
 /-- A variant of `span_induction` that combines `∀ x ∈ s, p x` and `∀ r x, p x → p (r • x)`
 into a single condition `∀ r, ∀ x ∈ s, p (r • x)`, which can be easier to verify. -/
 @[elab_as_elim]
-theorem closure_induction {p : M → Prop} (h : x ∈ span R s) (H0 : p 0)
-    (H1 : ∀ x y, p x → p y → p (x + y)) (H2 : ∀ r : R, ∀ x ∈ s, p (r • x)) : p x := by
+theorem closure_induction {p : M → Prop} (h : x ∈ span R s) (zero : p 0)
+    (add : ∀ x y, p x → p y → p (x + y)) (smul_mem : ∀ r : R, ∀ x ∈ s, p (r • x)) : p x := by
   rw [← mem_toAddSubmonoid, span_eq_closure] at h
-  refine AddSubmonoid.closure_induction h ?_ H0 H1
+  refine AddSubmonoid.closure_induction h ?_ zero add
   rintro _ ⟨r, -, m, hm, rfl⟩
-  exact H2 r m hm
+  exact smul_mem r m hm
 
 /-- A dependent version of `Submodule.closure_induction`. -/
 @[elab_as_elim]
 theorem closure_induction' {p : ∀ x, x ∈ span R s → Prop}
-    (H0 : p 0 (Submodule.zero_mem _))
-    (H1 : ∀ x hx y hy, p x hx → p y hy → p (x + y) (Submodule.add_mem _ ‹_› ‹_›))
-    (H2 : ∀ (r x) (h : x ∈ s), p (r • x) (Submodule.smul_mem _ _ <| subset_span h)) {x}
+    (zero : p 0 (Submodule.zero_mem _))
+    (add : ∀ x hx y hy, p x hx → p y hy → p (x + y) (Submodule.add_mem _ ‹_› ‹_›))
+    (smul_mem : ∀ (r x) (h : x ∈ s), p (r • x) (Submodule.smul_mem _ _ <| subset_span h)) {x}
     (hx : x ∈ span R s) : p x hx := by
   refine Exists.elim ?_ fun (hx : x ∈ span R s) (hc : p x hx) ↦ hc
-  refine closure_induction hx ⟨zero_mem _, H0⟩
+  refine closure_induction hx ⟨zero_mem _, zero⟩
     (fun x y hx hy ↦ Exists.elim hx fun hx' hx ↦
-      Exists.elim hy fun hy' hy ↦ ⟨add_mem hx' hy', H1 _ _ _ _ hx hy⟩)
-    fun r x hx ↦ ⟨smul_mem _ _ (subset_span hx), H2 r x hx⟩
+      Exists.elim hy fun hy' hy ↦ ⟨add_mem hx' hy', add _ _ _ _ hx hy⟩)
+    fun r x hx ↦ ⟨Submodule.smul_mem _ _ (subset_span hx), smul_mem r x hx⟩
 
 @[simp]
 theorem span_span_coe_preimage : span R (((↑) : span R s → M) ⁻¹' s) = ⊤ :=

ball for "bounded forall" and bex for "bounded exists" are from experience very confusing abbreviations. This PR renames them to forall_mem and exists_mem in the few Set lemma names that mention them.

Also deprecate ball_image_of_ball, mem_image_elim, mem_image_elim_on since those lemmas are duplicates of the renamed lemmas (apart from argument order and implicitness, which I am also fixing by making the binder in the RHS of forall_mem_image semi-implicit), have obscure names and are completely unused.

@@ -1112,7 +1112,7 @@ theorem ext_on {s : Set M} {f g : F} (hv : span R s = ⊤) (h : Set.EqOn f g s)
 each `v i`, then they are equal. -/
 theorem ext_on_range {ι : Type*} {v : ι → M} {f g : F} (hv : span R (Set.range v) = ⊤)
     (h : ∀ i, f (v i) = g (v i)) : f = g :=
-  ext_on hv (Set.forall_range_iff.2 h)
+  ext_on hv (Set.forall_mem_range.2 h)
 #align linear_map.ext_on_range LinearMap.ext_on_range
 
 end AddCommMonoid

• Prove isSemisimple_of_mem_adjoin: if two commuting endomorphisms of a finite-dimensional vector space over a perfect field are both semisimple, then every endomorphism in the algebra generated by them (in particular their product and sum) is semisimple.

• In the same file LinearAlgebra/Semisimple.lean, eq_zero_of_isNilpotent_isSemisimple and isSemisimple_of_squarefree_aeval_eq_zero are golfed, and IsSemisimple.minpoly_squarefree is proved

RingTheory/SimpleModule.lean:

• Define IsSemisimpleRing R to mean that R is a semisimple R-module. add properties of simple modules and a characterization (they are exactly the quotients of the ring by maximal left ideals).

• The annihilator of a semisimple module is a radical ideal.

• Any module over a semisimple ring is semisimple.

• A finite product of semisimple rings is semisimple.

• Any quotient of a semisimple ring is semisimple.

• Add Artin--Wedderburn as a TODO (proof_wanted).

• Order/Atoms.lean: add the instance from IsSimpleOrder to ComplementedLattice, so that IsSimpleModule → IsSemisimpleModule is automatically inferred.

Prerequisites for showing a product of semisimple rings is semisimple:

• Algebra/Module/Submodule/Map.lean: generalize orderIsoMapComap so that it only requires RingHomSurjective rather than RingHomInvPair

• Algebra/Ring/CompTypeclasses.lean, Mathlib/Algebra/Ring/Pi.lean, Algebra/Ring/Prod.lean: add RingHomSurjective instances

RingTheory/Artinian.lean:

• quotNilradicalEquivPi: the quotient of a commutative Artinian ring R by its nilradical is isomorphic to the (finite) product of its quotients by maximal ideals (therefore a product of fields). equivPi: if the ring is moreover reduced, then the ring itself is a product of fields. Deduce that R is a semisimple ring and both R and R[X] are decomposition monoids. Requires RingEquiv.quotientBot in RingTheory/Ideal/QuotientOperations.lean.

• Data/Polynomial/Eval.lean: the polynomial ring over a finite product of rings is isomorphic to the product of polynomial rings over individual rings. (Used to show R[X] is a decomposition monoid.)

Other necessary results:

• FieldTheory/Minpoly/Field.lean: the minimal polynomial of an element in a reduced algebra over a field is radical.

• RingTheory/PowerBasis.lean: generalize PowerBasis.finiteDimensional and rename it to .finite.

Annihilator stuff, some of which do not end up being used:

• RingTheory/Ideal/Operations.lean: define Module.annihilator and redefine Submodule.annihilator in terms of it; add lemmas, including one that says an arbitrary intersection of radical ideals is radical. The new lemma Ideal.isRadical_iff_pow_one_lt depends on pow_imp_self_of_one_lt in Mathlib/Data/Nat/Interval.lean, which is also used to golf the proof of isRadical_iff_pow_one_lt.

• Algebra/Module/Torsion.lean: add a lemma and an instance (unused)

• Data/Polynomial/Module/Basic.lean: add a def (unused) and a lemma

• LinearAlgebra/AnnihilatingPolynomial.lean: add lemma span_minpoly_eq_annihilator

Some results about idempotent linear maps (projections) and idempotent elements, used to show that any (left) ideal in a semisimple ring is spanned by an idempotent element (unused):

• LinearAlgebra/Projection.lean: add def isIdempotentElemEquiv

• LinearAlgebra/Span.lean: add two lemmas

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

@@ -5,6 +5,7 @@ Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Fréd
   Heather Macbeth
 -/
 import Mathlib.Algebra.Module.Submodule.RestrictScalars
+import Mathlib.Algebra.Ring.Idempotents
 import Mathlib.Data.Set.Pointwise.SMul
 import Mathlib.LinearAlgebra.Basic
 import Mathlib.Order.CompactlyGenerated.Basic
@@ -52,6 +53,20 @@ def span (s : Set M) : Submodule R M :=
   sInf { p | s ⊆ p }
 #align submodule.span Submodule.span
 
+variable {R}
+
+-- Porting note: renamed field to `principal'` and added `principal` to fix explicit argument
+/-- An `R`-submodule of `M` is principal if it is generated by one element. -/
+@[mk_iff]
+class IsPrincipal (S : Submodule R M) : Prop where
+  principal' : ∃ a, S = span R {a}
+#align submodule.is_principal Submodule.IsPrincipal
+
+theorem IsPrincipal.principal (S : Submodule R M) [S.IsPrincipal] :
+    ∃ a, S = span R {a} :=
+  Submodule.IsPrincipal.principal'
+#align submodule.is_principal.principal Submodule.IsPrincipal.principal
+
 end
 
 variable {s t : Set M}
@@ -1019,7 +1034,7 @@ section
 variable (R) (M) [Semiring R] [AddCommMonoid M] [Module R M]
 
 /-- Given an element `x` of a module `M` over `R`, the natural map from
-    `R` to scalar multiples of `x`.-/
+    `R` to scalar multiples of `x`. See also `LinearMap.ringLmapEquivSelf`. -/
 @[simps!]
 def toSpanSingleton (x : M) : R →ₗ[R] M :=
   LinearMap.id.smulRight x
@@ -1043,6 +1058,19 @@ theorem toSpanSingleton_zero : toSpanSingleton R M 0 = 0 := by
   simp
 #align linear_map.to_span_singleton_zero LinearMap.toSpanSingleton_zero
 
+variable {R M}
+
+theorem toSpanSingleton_isIdempotentElem_iff {e : R} :
+    IsIdempotentElem (toSpanSingleton R R e) ↔ IsIdempotentElem e := by
+  simp_rw [IsIdempotentElem, ext_iff, mul_apply, toSpanSingleton_apply, smul_eq_mul, mul_assoc]
+  exact ⟨fun h ↦ by conv_rhs => rw [← one_mul e, ← h, one_mul], fun h _ ↦ by rw [h]⟩
+
+theorem isIdempotentElem_apply_one_iff {f : Module.End R R} :
+    IsIdempotentElem (f 1) ↔ IsIdempotentElem f := by
+  rw [IsIdempotentElem, ← smul_eq_mul, ← map_smul, smul_eq_mul, mul_one, IsIdempotentElem, ext_iff]
+  simp_rw [mul_apply]
+  exact ⟨fun h r ↦ by rw [← mul_one r, ← smul_eq_mul, map_smul, map_smul, h], (· 1)⟩
+
 end
 
 section AddCommMonoid

In order to improve the ergonomics of the induction tactic, this renames the arguments of:

• ExteriorAlgebra.induction
• TensorAlgebra.induction
• CliffordAlgebra.induction
• CliffordAlgebra.left_induction
• CliffordAlgebra.right_induction
• CliffordAlgebra.even_induction
• CliffordAlgebra.odd_induction
• Submodule.iSup_induction'
• Submodule.pow_induction_on_left'
• Submodule.pow_induction_on_right'

This is slightly awkward for name-resolution within these induction principles, as the argument names end up clashing with the function they are about. Thankfully, this pain is not transferred to the caller using induction _ using _.

@@ -692,16 +692,16 @@ theorem iSup_induction {ι : Sort*} (p : ι → Submodule R M) {C : M → Prop}
 /-- A dependent version of `submodule.iSup_induction`. -/
 @[elab_as_elim]
 theorem iSup_induction' {ι : Sort*} (p : ι → Submodule R M) {C : ∀ x, (x ∈ ⨆ i, p i) → Prop}
-    (hp : ∀ (i) (x) (hx : x ∈ p i), C x (mem_iSup_of_mem i hx)) (h0 : C 0 (zero_mem _))
-    (hadd : ∀ x y hx hy, C x hx → C y hy → C (x + y) (add_mem ‹_› ‹_›)) {x : M}
+    (mem : ∀ (i) (x) (hx : x ∈ p i), C x (mem_iSup_of_mem i hx)) (zero : C 0 (zero_mem _))
+    (add : ∀ x y hx hy, C x hx → C y hy → C (x + y) (add_mem ‹_› ‹_›)) {x : M}
     (hx : x ∈ ⨆ i, p i) : C x hx := by
   refine' Exists.elim _ fun (hx : x ∈ ⨆ i, p i) (hc : C x hx) => hc
   refine' iSup_induction p (C := fun x : M ↦ ∃ (hx : x ∈ ⨆ i, p i), C x hx) hx
     (fun i x hx => _) _ fun x y => _
-  · exact ⟨_, hp _ _ hx⟩
-  · exact ⟨_, h0⟩
+  · exact ⟨_, mem _ _ hx⟩
+  · exact ⟨_, zero⟩
   · rintro ⟨_, Cx⟩ ⟨_, Cy⟩
-    exact ⟨_, hadd _ _ _ _ Cx Cy⟩
+    exact ⟨_, add _ _ _ _ Cx Cy⟩
 #align submodule.supr_induction' Submodule.iSup_induction'
 
 theorem singleton_span_isCompactElement (x : M) :

Dependent induction did not support this attribute in Lean 3.

A few downstream applys change to refine as a result. A future PR could replace some of these with induction.

@@ -172,6 +172,7 @@ theorem span_induction₂ {p : M → M → Prop} {a b : M} (ha : a ∈ Submodule
     (H0_left b) (fun x₁ x₂ => Hadd_left x₁ x₂ b) fun r x => Hsmul_left r x b
 
 /-- A dependent version of `Submodule.span_induction`. -/
+@[elab_as_elim]
 theorem span_induction' {p : ∀ x, x ∈ span R s → Prop}
     (Hs : ∀ (x) (h : x ∈ s), p x (subset_span h))
     (H0 : p 0 (Submodule.zero_mem _))
@@ -209,6 +210,7 @@ theorem closure_induction {p : M → Prop} (h : x ∈ span R s) (H0 : p 0)
   exact H2 r m hm
 
 /-- A dependent version of `Submodule.closure_induction`. -/
+@[elab_as_elim]
 theorem closure_induction' {p : ∀ x, x ∈ span R s → Prop}
     (H0 : p 0 (Submodule.zero_mem _))
     (H1 : ∀ x hx y hy, p x hx → p y hy → p (x + y) (Submodule.add_mem _ ‹_› ‹_›))

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

@@ -60,7 +60,7 @@ theorem mem_span : x ∈ span R s ↔ ∀ p : Submodule R M, s ⊆ p → x ∈ p
   mem_iInter₂
 #align submodule.mem_span Submodule.mem_span
 
-@[aesop safe 20 apply (rule_sets [SetLike])]
+@[aesop safe 20 apply (rule_sets := [SetLike])]
 theorem subset_span : s ⊆ span R s := fun _ h => mem_span.2 fun _ hp => hp h
 #align submodule.subset_span Submodule.subset_span
 

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -699,7 +699,7 @@ theorem iSup_induction' {ι : Sort*} (p : ι → Submodule R M) {C : ∀ x, (x 
   · exact ⟨_, hp _ _ hx⟩
   · exact ⟨_, h0⟩
   · rintro ⟨_, Cx⟩ ⟨_, Cy⟩
-    refine' ⟨_, hadd _ _ _ _ Cx Cy⟩
+    exact ⟨_, hadd _ _ _ _ Cx Cy⟩
 #align submodule.supr_induction' Submodule.iSup_induction'
 
 theorem singleton_span_isCompactElement (x : M) :
@@ -839,7 +839,7 @@ theorem prod_sup_prod : prod p q₁ ⊔ prod p' q₁' = prod (p ⊔ p') (q₁ 
   simp [SetLike.le_def]; intro xx yy hxx hyy
   rcases mem_sup.1 hxx with ⟨x, hx, x', hx', rfl⟩
   rcases mem_sup.1 hyy with ⟨y, hy, y', hy', rfl⟩
-  refine' mem_sup.2 ⟨(x, y), ⟨hx, hy⟩, (x', y'), ⟨hx', hy'⟩, rfl⟩
+  exact mem_sup.2 ⟨(x, y), ⟨hx, hy⟩, (x', y'), ⟨hx', hy'⟩, rfl⟩
 #align submodule.prod_sup_prod Submodule.prod_sup_prod
 
 end AddCommMonoid

@@ -919,6 +919,38 @@ lemma _root_.LinearMap.range_domRestrict_eq_range_iff {f : M →ₛₗ[τ₁₂]
   rw [← hf]
   exact LinearMap.range_domRestrict_eq_range_iff
 
+@[simp]
+lemma biSup_comap_subtype_eq_top {ι : Type*} (s : Set ι) (p : ι → Submodule R M) :
+    ⨆ i ∈ s, (p i).comap (⨆ i ∈ s, p i).subtype = ⊤ := by
+  refine eq_top_iff.mpr fun ⟨x, hx⟩ _ ↦ ?_
+  suffices x ∈ (⨆ i ∈ s, (p i).comap (⨆ i ∈ s, p i).subtype).map (⨆ i ∈ s, (p i)).subtype by
+    obtain ⟨y, hy, rfl⟩ := Submodule.mem_map.mp this
+    exact hy
+  suffices ∀ i ∈ s, (comap (⨆ i ∈ s, p i).subtype (p i)).map (⨆ i ∈ s, p i).subtype = p i by
+    simpa only [map_iSup, biSup_congr this]
+  intro i hi
+  rw [map_comap_eq, range_subtype, inf_eq_right]
+  exact le_biSup p hi
+
+lemma biSup_comap_eq_top_of_surjective {ι : Type*} (s : Set ι) (hs : s.Nonempty)
+    (p : ι → Submodule R₂ M₂) (hp : ⨆ i ∈ s, p i = ⊤)
+    (f : M →ₛₗ[τ₁₂] M₂) (hf : Surjective f) :
+    ⨆ i ∈ s, (p i).comap f = ⊤ := by
+  obtain ⟨k, hk⟩ := hs
+  suffices (⨆ i ∈ s, (p i).comap f) ⊔ LinearMap.ker f = ⊤ by
+    rw [← this, left_eq_sup]; exact le_trans f.ker_le_comap (le_biSup (fun i ↦ (p i).comap f) hk)
+  rw [iSup_subtype'] at hp ⊢
+  rw [← comap_map_eq, map_iSup_comap_of_sujective hf, hp, comap_top]
+
+lemma biSup_comap_eq_top_of_range_eq_biSup
+    {R R₂ : Type*} [Ring R] [Ring R₂] {τ₁₂ : R →+* R₂} [RingHomSurjective τ₁₂]
+    [Module R M] [Module R₂ M₂] {ι : Type*} (s : Set ι) (hs : s.Nonempty)
+    (p : ι → Submodule R₂ M₂) (f : M →ₛₗ[τ₁₂] M₂) (hf : LinearMap.range f = ⨆ i ∈ s, p i) :
+    ⨆ i ∈ s, (p i).comap f = ⊤ := by
+  suffices ⨆ i ∈ s, (p i).comap (LinearMap.range f).subtype = ⊤ by
+    rw [← biSup_comap_eq_top_of_surjective s hs _ this _ f.surjective_rangeRestrict]; rfl
+  exact hf ▸ biSup_comap_subtype_eq_top s p
+
 end AddCommGroup
 
 section DivisionRing

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

@@ -998,7 +998,7 @@ theorem span_singleton_eq_range (x : M) : (R ∙ x) = range (toSpanSingleton R M
     exact mem_span_singleton
 #align linear_map.span_singleton_eq_range LinearMap.span_singleton_eq_range
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem toSpanSingleton_one (x : M) : toSpanSingleton R M x 1 = x :=
   one_smul _ _
 #align linear_map.to_span_singleton_one LinearMap.toSpanSingleton_one

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -933,8 +933,8 @@ theorem wcovBy_span_singleton_sup (x : V) (p : Submodule K V) : WCovBy p ((K ∙
     simpa [mem_sup, mem_span_singleton] using hqp.le hyq
   rcases eq_or_ne c 0 with rfl | hc
   · simp [hz] at hyp
-  · have : x ∈ q
-    · rwa [q.add_mem_iff_left (hpq.le hz), q.smul_mem_iff hc] at hyq
+  · have : x ∈ q := by
+      rwa [q.add_mem_iff_left (hpq.le hz), q.smul_mem_iff hc] at hyq
     simp [hpq.le, this]
 
 /-- There is no vector subspace between `p` and `(K ∙ x) ⊔ p`, `CovBy` version. -/

@@ -1099,12 +1099,14 @@ def toSpanNonzeroSingleton : R ≃ₗ[R] R ∙ x :=
     (LinearEquiv.ofEq (range <| toSpanSingleton R M x) (R ∙ x) (span_singleton_eq_range R M x).symm)
 #align linear_equiv.to_span_nonzero_singleton LinearEquiv.toSpanNonzeroSingleton
 
+@[simp] theorem toSpanNonzeroSingleton_apply (t : R) :
+    LinearEquiv.toSpanNonzeroSingleton R M x h t =
+      (⟨t • x, Submodule.smul_mem _ _ (Submodule.mem_span_singleton_self x)⟩ : R ∙ x) := by
+  rfl
+
 theorem toSpanNonzeroSingleton_one :
     LinearEquiv.toSpanNonzeroSingleton R M x h 1 =
-      (⟨x, Submodule.mem_span_singleton_self x⟩ : R ∙ x) := by
-  apply SetLike.coe_eq_coe.mp
-  have : ↑(toSpanNonzeroSingleton R M x h 1) = toSpanSingleton R M x 1 := rfl
-  rw [this, toSpanSingleton_one, Submodule.coe_mk]
+      (⟨x, Submodule.mem_span_singleton_self x⟩ : R ∙ x) := by simp
 #align linear_equiv.to_span_nonzero_singleton_one LinearEquiv.toSpanNonzeroSingleton_one
 
 /-- Given a nonzero element `x` of a torsion-free module `M` over a ring `R`, the natural

This cleans up instances of

⟨ foo, bar⟩

and

⟨foo, bar ⟩

where spaces a on the inside one side, but not on the other side. Fixing this by removing the extra space.

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

@@ -154,7 +154,7 @@ preserved under addition and scalar multiplication, then `p` holds for all eleme
 @[elab_as_elim]
 theorem span_induction {p : M → Prop} (h : x ∈ span R s) (Hs : ∀ x ∈ s, p x) (H0 : p 0)
     (H1 : ∀ x y, p x → p y → p (x + y)) (H2 : ∀ (a : R) (x), p x → p (a • x)) : p x :=
-  ((@span_le (p := ⟨ ⟨⟨p, by intros x y; exact H1 x y⟩, H0⟩, H2⟩)) s).2 Hs h
+  ((@span_le (p := ⟨⟨⟨p, by intros x y; exact H1 x y⟩, H0⟩, H2⟩)) s).2 Hs h
 #align submodule.span_induction Submodule.span_induction
 
 /-- An induction principle for span membership. This is a version of `Submodule.span_induction`

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>

@@ -40,7 +40,8 @@ variable {x : M} (p p' : Submodule R M)
 
 variable [Semiring R₂] {σ₁₂ : R →+* R₂}
 
-variable [AddCommMonoid M₂] [Module R₂ M₂] {F : Type*} [SemilinearMapClass F σ₁₂ M M₂]
+variable [AddCommMonoid M₂] [Module R₂ M₂]
+variable {F : Type*} [FunLike F M M₂] [SemilinearMapClass F σ₁₂ M M₂]
 
 section
 
@@ -613,12 +614,17 @@ theorem span_singleton_eq_span_singleton {R M : Type*} [Ring R] [AddCommGroup M]
     exact (span_singleton_group_smul_eq _ _ _).symm
 #align submodule.span_singleton_eq_span_singleton Submodule.span_singleton_eq_span_singleton
 
-@[simp]
+-- Should be `@[simp]` but doesn't fire due to `lean4#3701`.
 theorem span_image [RingHomSurjective σ₁₂] (f : F) :
     span R₂ (f '' s) = map f (span R s) :=
   (map_span f s).symm
 #align submodule.span_image Submodule.span_image
 
+@[simp] -- Should be replaced with `Submodule.span_image` when `lean4#3701` is fixed.
+theorem span_image' [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) :
+    span R₂ (f '' s) = map f (span R s) :=
+  span_image _
+
 theorem apply_mem_span_image_of_mem_span [RingHomSurjective σ₁₂] (f : F) {x : M}
     {s : Set M} (h : x ∈ Submodule.span R s) : f x ∈ Submodule.span R₂ (f '' s) := by
   rw [Submodule.span_image]
@@ -878,7 +884,7 @@ variable [AddCommGroup M] [Module R M] [AddCommGroup M₂] [Module R₂ M₂]
 
 variable {τ₁₂ : R →+* R₂} [RingHomSurjective τ₁₂]
 
-variable {F : Type*} [sc : SemilinearMapClass F τ₁₂ M M₂]
+variable {F : Type*} [FunLike F M M₂] [SemilinearMapClass F τ₁₂ M M₂]
 
 theorem comap_map_eq (f : F) (p : Submodule R M) : comap f (map f p) = p ⊔ LinearMap.ker f := by
   refine' le_antisymm _ (sup_le (le_comap_map _ _) (comap_mono bot_le))
@@ -953,7 +959,7 @@ variable [Module R M] [Module R₂ M₂]
 
 variable {τ₁₂ : R →+* R₂} [RingHomSurjective τ₁₂]
 
-variable {F : Type*} [sc : SemilinearMapClass F τ₁₂ M M₂]
+variable {F : Type*} [FunLike F M M₂] [SemilinearMapClass F τ₁₂ M M₂]
 
 protected theorem map_le_map_iff (f : F) {p p'} : map f p ≤ map f p' ↔ p ≤ p' ⊔ ker f := by
   rw [map_le_iff_le_comap, Submodule.comap_map_eq]
@@ -1011,7 +1017,7 @@ variable [Semiring R] [AddCommMonoid M] [Module R M]
 
 variable [Semiring R₂] [AddCommMonoid M₂] [Module R₂ M₂]
 
-variable {F : Type*} {σ₁₂ : R →+* R₂} [SemilinearMapClass F σ₁₂ M M₂]
+variable {F : Type*} {σ₁₂ : R →+* R₂} [FunLike F M M₂] [SemilinearMapClass F σ₁₂ M M₂]
 
 /-- Two linear maps are equal on `Submodule.span s` iff they are equal on `s`. -/
 theorem eqOn_span_iff {s : Set M} {f g : F} : Set.EqOn f g (span R s) ↔ Set.EqOn f g s := by

• depends on: #9830
• depends on: #9772
• depends on: #9996

This checks files for unused imports. The output here is piped through gh-problem-matcher-wrap so that it will show up as annotations.

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

@@ -5,6 +5,7 @@ Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Fréd
   Heather Macbeth
 -/
 import Mathlib.Algebra.Module.Submodule.RestrictScalars
+import Mathlib.Data.Set.Pointwise.SMul
 import Mathlib.LinearAlgebra.Basic
 import Mathlib.Order.CompactlyGenerated.Basic
 import Mathlib.Order.OmegaCompletePartialOrder

This reworks the location of the lemmas from #10086, by moving them to a new Mathlib.Order.CompactlyGenerated.Intervals file. The existing Mathlib.Order.CompactlyGenerated is moved to Mathlib.Order.CompactlyGenerated.Basic for consistency.

@@ -6,7 +6,7 @@ Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Fréd
 -/
 import Mathlib.Algebra.Module.Submodule.RestrictScalars
 import Mathlib.LinearAlgebra.Basic
-import Mathlib.Order.CompactlyGenerated
+import Mathlib.Order.CompactlyGenerated.Basic
 import Mathlib.Order.OmegaCompletePartialOrder
 
 #align_import linear_algebra.span from "leanprover-community/mathlib"@"10878f6bf1dab863445907ab23fbfcefcb5845d0"

Since Submodule.map requires surjectivity of the RingHom, the new lemmas have to be stated this way. (The RingHom is frobenius in my intended application, which is not necessarily surjective.)

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

@@ -92,20 +92,24 @@ theorem span_coe_eq_restrictScalars [Semiring S] [SMul S R] [Module S M] [IsScal
   span_eq (p.restrictScalars S)
 #align submodule.span_coe_eq_restrict_scalars Submodule.span_coe_eq_restrictScalars
 
+/-- A version of `Submodule.map_span_le` that does not require the `RingHomSurjective`
+assumption. -/
+theorem image_span_subset (f : F) (s : Set M) (N : Submodule R₂ M₂) :
+    f '' span R s ⊆ N ↔ ∀ m ∈ s, f m ∈ N := image_subset_iff.trans <| span_le (p := N.comap f)
+
+theorem image_span_subset_span (f : F) (s : Set M) : f '' span R s ⊆ span R₂ (f '' s) :=
+  (image_span_subset f s _).2 fun x hx ↦ subset_span ⟨x, hx, rfl⟩
+
 theorem map_span [RingHomSurjective σ₁₂] (f : F) (s : Set M) :
     (span R s).map f = span R₂ (f '' s) :=
-  Eq.symm <|
-    span_eq_of_le _ (Set.image_subset f subset_span) <|
-      map_le_iff_le_comap.2 <| span_le.2 fun x hx => subset_span ⟨x, hx, rfl⟩
+  Eq.symm <| span_eq_of_le _ (Set.image_subset f subset_span) (image_span_subset_span f s)
 #align submodule.map_span Submodule.map_span
 
 alias _root_.LinearMap.map_span := Submodule.map_span
 #align linear_map.map_span LinearMap.map_span
 
 theorem map_span_le [RingHomSurjective σ₁₂] (f : F) (s : Set M) (N : Submodule R₂ M₂) :
-    map f (span R s) ≤ N ↔ ∀ m ∈ s, f m ∈ N := by
-  rw [map_span, span_le, Set.image_subset_iff]
-  exact Iff.rfl
+    map f (span R s) ≤ N ↔ ∀ m ∈ s, f m ∈ N := image_span_subset f s N
 #align submodule.map_span_le Submodule.map_span_le
 
 alias _root_.LinearMap.map_span_le := Submodule.map_span_le

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>

@@ -1032,7 +1032,7 @@ theorem eqOn_span {s : Set M} {f g : F} (H : Set.EqOn f g s) ⦃x⦄ (h : x ∈
 /-- If `s` generates the whole module and linear maps `f`, `g` are equal on `s`, then they are
 equal. -/
 theorem ext_on {s : Set M} {f g : F} (hv : span R s = ⊤) (h : Set.EqOn f g s) : f = g :=
-  FunLike.ext _ _ fun _ => eqOn_span h (eq_top_iff'.1 hv _)
+  DFunLike.ext _ _ fun _ => eqOn_span h (eq_top_iff'.1 hv _)
 #align linear_map.ext_on LinearMap.ext_on
 
 /-- If the range of `v : ι → M` generates the whole module and linear maps `f`, `g` are equal at

This is a straight copy-paste: there are no new lemmas and nothing has been removed or renamed. The only changes are a few lemmas where argument explicitness or ordering has changed (and where it did not seem to make sense to replicate the old argument explicitness or ordering).

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Frédéric Dupuis,
   Heather Macbeth
 -/
+import Mathlib.Algebra.Module.Submodule.RestrictScalars
 import Mathlib.LinearAlgebra.Basic
 import Mathlib.Order.CompactlyGenerated
 import Mathlib.Order.OmegaCompletePartialOrder

Rename

• Covby → CovBy, Wcovby → WCovBy
• *covby* → *covBy*
• wcovby.finset_val → WCovBy.finset_val, wcovby.finset_coe → WCovBy.finset_coe
• Covby.is_coatom → CovBy.isCoatom

@@ -913,8 +913,8 @@ section DivisionRing
 
 variable [DivisionRing K] [AddCommGroup V] [Module K V]
 
-/-- There is no vector subspace between `p` and `(K ∙ x) ⊔ p`, `Wcovby` version. -/
-theorem wcovby_span_singleton_sup (x : V) (p : Submodule K V) : Wcovby p ((K ∙ x) ⊔ p) := by
+/-- There is no vector subspace between `p` and `(K ∙ x) ⊔ p`, `WCovBy` version. -/
+theorem wcovBy_span_singleton_sup (x : V) (p : Submodule K V) : WCovBy p ((K ∙ x) ⊔ p) := by
   refine ⟨le_sup_right, fun q hpq hqp ↦ hqp.not_le ?_⟩
   rcases SetLike.exists_of_lt hpq with ⟨y, hyq, hyp⟩
   obtain ⟨c, z, hz, rfl⟩ : ∃ c : K, ∃ z ∈ p, c • x + z = y := by
@@ -925,9 +925,9 @@ theorem wcovby_span_singleton_sup (x : V) (p : Submodule K V) : Wcovby p ((K ∙
     · rwa [q.add_mem_iff_left (hpq.le hz), q.smul_mem_iff hc] at hyq
     simp [hpq.le, this]
 
-/-- There is no vector subspace between `p` and `(K ∙ x) ⊔ p`, `Covby` version. -/
-theorem covby_span_singleton_sup {x : V} {p : Submodule K V} (h : x ∉ p) : Covby p ((K ∙ x) ⊔ p) :=
-  ⟨by simpa, (wcovby_span_singleton_sup _ _).2⟩
+/-- There is no vector subspace between `p` and `(K ∙ x) ⊔ p`, `CovBy` version. -/
+theorem covBy_span_singleton_sup {x : V} {p : Submodule K V} (h : x ∉ p) : CovBy p ((K ∙ x) ⊔ p) :=
+  ⟨by simpa, (wcovBy_span_singleton_sup _ _).2⟩
 
 end DivisionRing
 

See Zulip thread for the discussion.

@@ -1084,7 +1084,7 @@ def toSpanNonzeroSingleton : R ≃ₗ[R] R ∙ x :=
   LinearEquiv.trans
     (LinearEquiv.ofInjective (LinearMap.toSpanSingleton R M x)
       (ker_eq_bot.1 <| ker_toSpanSingleton R M h))
-    (LinearEquiv.ofEq (range $ toSpanSingleton R M x) (R ∙ x) (span_singleton_eq_range R M x).symm)
+    (LinearEquiv.ofEq (range <| toSpanSingleton R M x) (R ∙ x) (span_singleton_eq_range R M x).symm)
 #align linear_equiv.to_span_nonzero_singleton LinearEquiv.toSpanNonzeroSingleton
 
 theorem toSpanNonzeroSingleton_one :

Add span_eq_closure and closure_induction which say that Submodule.span R s is generated by R • s as an AddSubmonoid. I feel that the existing span_induction should be replaced by closure_induction as the latter is stronger, and allow us to remove the commutativity condition in span_smul_of_span_eq_top in Algebra/Tower and generalize Module.Finite.trans to allow a non-commutative base ring.

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

@@ -180,6 +180,39 @@ theorem span_induction' {p : ∀ x, x ∈ span R s → Prop}
       fun r x hx => Exists.elim hx fun hx' hx => ⟨smul_mem _ _ hx', H2 r _ _ hx⟩
 #align submodule.span_induction' Submodule.span_induction'
 
+open AddSubmonoid in
+theorem span_eq_closure {s : Set M} : (span R s).toAddSubmonoid = closure (@univ R • s) := by
+  refine le_antisymm
+    (fun x hx ↦ span_induction hx (fun x hx ↦ subset_closure ⟨1, trivial, x, hx, one_smul R x⟩)
+      (zero_mem _) (fun _ _ ↦ add_mem) fun r m hm ↦ closure_induction hm ?_ ?_ fun _ _ h h' ↦ ?_)
+    (closure_le.2 ?_)
+  · rintro _ ⟨r, -, m, hm, rfl⟩; exact smul_mem _ _ (subset_span hm)
+  · rintro _ ⟨r', -, m, hm, rfl⟩; exact subset_closure ⟨r * r', trivial, m, hm, mul_smul r r' m⟩
+  · rw [smul_zero]; apply zero_mem
+  · rw [smul_add]; exact add_mem h h'
+
+/-- A variant of `span_induction` that combines `∀ x ∈ s, p x` and `∀ r x, p x → p (r • x)`
+into a single condition `∀ r, ∀ x ∈ s, p (r • x)`, which can be easier to verify. -/
+@[elab_as_elim]
+theorem closure_induction {p : M → Prop} (h : x ∈ span R s) (H0 : p 0)
+    (H1 : ∀ x y, p x → p y → p (x + y)) (H2 : ∀ r : R, ∀ x ∈ s, p (r • x)) : p x := by
+  rw [← mem_toAddSubmonoid, span_eq_closure] at h
+  refine AddSubmonoid.closure_induction h ?_ H0 H1
+  rintro _ ⟨r, -, m, hm, rfl⟩
+  exact H2 r m hm
+
+/-- A dependent version of `Submodule.closure_induction`. -/
+theorem closure_induction' {p : ∀ x, x ∈ span R s → Prop}
+    (H0 : p 0 (Submodule.zero_mem _))
+    (H1 : ∀ x hx y hy, p x hx → p y hy → p (x + y) (Submodule.add_mem _ ‹_› ‹_›))
+    (H2 : ∀ (r x) (h : x ∈ s), p (r • x) (Submodule.smul_mem _ _ <| subset_span h)) {x}
+    (hx : x ∈ span R s) : p x hx := by
+  refine Exists.elim ?_ fun (hx : x ∈ span R s) (hc : p x hx) ↦ hc
+  refine closure_induction hx ⟨zero_mem _, H0⟩
+    (fun x y hx hy ↦ Exists.elim hx fun hx' hx ↦
+      Exists.elim hy fun hy' hy ↦ ⟨add_mem hx' hy', H1 _ _ _ _ hx hy⟩)
+    fun r x hx ↦ ⟨smul_mem _ _ (subset_span hx), H2 r x hx⟩
+
 @[simp]
 theorem span_span_coe_preimage : span R (((↑) : span R s → M) ⁻¹' s) = ⊤ :=
   eq_top_iff.2 fun x ↦ Subtype.recOn x fun x hx _ ↦ by

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

@@ -673,7 +673,7 @@ theorem finset_span_isCompactElement (S : Finset M) :
   simp only [Finset.mem_coe]
   rw [← Finset.sup_eq_iSup]
   exact
-    CompleteLattice.finset_sup_compact_of_compact S fun x _ => singleton_span_isCompactElement x
+    CompleteLattice.isCompactElement_finsetSup S fun x _ => singleton_span_isCompactElement x
 #align submodule.finset_span_is_compact_element Submodule.finset_span_isCompactElement
 
 /-- The span of a finite subset is compact in the lattice of submodules. -/

Follow-up #9184

@@ -692,8 +692,8 @@ instance : IsCompactlyGenerated (Submodule R M) :=
 
 /-- A submodule is equal to the supremum of the spans of the submodule's nonzero elements. -/
 theorem submodule_eq_sSup_le_nonzero_spans (p : Submodule R M) :
-    p = sSup { T : Submodule R M | ∃ (m : M) (_ : m ∈ p) (_ : m ≠ 0), T = span R {m} } := by
-  let S := { T : Submodule R M | ∃ (m : M) (_ : m ∈ p) (_ : m ≠ 0), T = span R {m} }
+    p = sSup { T : Submodule R M | ∃ m ∈ p, m ≠ 0 ∧ T = span R {m} } := by
+  let S := { T : Submodule R M | ∃ m ∈ p, m ≠ 0 ∧ T = span R {m} }
   apply le_antisymm
   · intro m hm
     by_cases h : m = 0

A collection of loosely-related lemmas, split out from other work in the hopes of simplifying review.

@@ -190,6 +190,11 @@ theorem span_span_coe_preimage : span R (((↑) : span R s → M) ⁻¹' s) = 
     · exact smul_mem _ _
 #align submodule.span_span_coe_preimage Submodule.span_span_coe_preimage
 
+@[simp]
+lemma span_setOf_mem_eq_top :
+    span R {x : span R s | (x : M) ∈ s} = ⊤ :=
+  span_span_coe_preimage
+
 theorem span_nat_eq_addSubmonoid_closure (s : Set M) :
     (span ℕ s).toAddSubmonoid = AddSubmonoid.closure s := by
   refine' Eq.symm (AddSubmonoid.closure_eq_of_le subset_span _)

This reduces the file from ~2600 lines to ~1600 lines.

Co-authored-by: Vierkantor <vierkantor@vierkantor.com> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

@@ -7,7 +7,6 @@ Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Fréd
 import Mathlib.LinearAlgebra.Basic
 import Mathlib.Order.CompactlyGenerated
 import Mathlib.Order.OmegaCompletePartialOrder
-import Mathlib.Tactic.Ring
 
 #align_import linear_algebra.span from "leanprover-community/mathlib"@"10878f6bf1dab863445907ab23fbfcefcb5845d0"
 

@@ -305,17 +305,15 @@ theorem span_smul_eq_of_isUnit (s : Set M) (r : R) (hr : IsUnit r) : span R (r 
 #align submodule.span_smul_eq_of_is_unit Submodule.span_smul_eq_of_isUnit
 
 @[simp]
-theorem coe_iSup_of_directed {ι} [hι : Nonempty ι] (S : ι → Submodule R M)
-    (H : Directed (· ≤ ·) S) : ((iSup S : Submodule R M) : Set M) = ⋃ i, S i := by
-  refine' Subset.antisymm _ (iUnion_subset <| le_iSup S)
-  suffices (span R (⋃ i, (S i : Set M)) : Set M) ⊆ ⋃ i : ι, ↑(S i) by
-    simpa only [span_iUnion, span_eq] using this
-  refine' fun x hx => span_induction hx (fun _ => id) _ _ _ <;> simp only [mem_iUnion, exists_imp]
-  · exact hι.elim fun i => ⟨i, (S i).zero_mem⟩
-  · intro x y i hi j hj
-    rcases H i j with ⟨k, ik, jk⟩
-    exact ⟨k, add_mem (ik hi) (jk hj)⟩
-  · exact fun a x i hi => ⟨i, smul_mem _ a hi⟩
+theorem coe_iSup_of_directed {ι} [Nonempty ι] (S : ι → Submodule R M)
+    (H : Directed (· ≤ ·) S) : ((iSup S: Submodule R M) : Set M) = ⋃ i, S i :=
+  let s : Submodule R M :=
+    { __ := AddSubmonoid.copy _ _ (AddSubmonoid.coe_iSup_of_directed H).symm
+      smul_mem' := fun r _ hx ↦ have ⟨i, hi⟩ := Set.mem_iUnion.mp hx
+        Set.mem_iUnion.mpr ⟨i, (S i).smul_mem' r hi⟩ }
+  have : iSup S = s := le_antisymm
+    (iSup_le fun i ↦ le_iSup (fun i ↦ (S i : Set M)) i) (Set.iUnion_subset fun _ ↦ le_iSup S _)
+  this.symm ▸ rfl
 #align submodule.coe_supr_of_directed Submodule.coe_iSup_of_directed
 
 @[simp]

This creates a new aesop rule set called SetLike to house lemmas about membership in subobjects.

Lemmas like pow_mem should be included in the rule set:

@[to_additive (attr := aesop safe apply (rule_sets [SetLike]))]
theorem pow_mem {M A} [Monoid M] [SetLike A M] [SubmonoidClass A M] {S : A} {x : M}
(hx : x ∈ S) : ∀ n : ℕ, x ^ n ∈ S

Lemmas about closures, like AddSubmonoid.closure should be included in the rule set, but they should be assigned a penalty (here we choose 20 throughout) so that they are not attempted before the general purpose ones like pow_mem.

@[to_additive (attr := simp, aesop safe 20 apply (rule_sets [SetLike]))
  "The `AddSubmonoid` generated by a set includes the set."]
theorem subset_closure : s ⊆ closure s := fun _ hx => mem_closure.2 fun _ hS => hS hx

In order for aesop to make effective use of AddSubmonoid.closure it needs the following new lemma.

@[aesop 5% apply (rule_sets [SetLike])]
lemma mem_of_subset {s : Set B} (hp : s ⊆ p) {x : B} (hx : x ∈ s) : x ∈ p := hp hx

Note: this lemma is marked as very unsafe (5%) because it will apply whenever the goal is of the form x ∈ p where p is any term of a SetLike instance; and moreover, it will create s as a metavariable, which is in general a terrible idea, but necessary for the reason mentioned above.

@@ -58,6 +58,7 @@ theorem mem_span : x ∈ span R s ↔ ∀ p : Submodule R M, s ⊆ p → x ∈ p
   mem_iInter₂
 #align submodule.mem_span Submodule.mem_span
 
+@[aesop safe 20 apply (rule_sets [SetLike])]
 theorem subset_span : s ⊆ span R s := fun _ h => mem_span.2 fun _ hp => hp h
 #align submodule.subset_span Submodule.subset_span
 

Replace rcases( with rcases (. Same thing for convert( and congrm(. No other change.

@@ -683,7 +683,7 @@ instance : IsCompactlyGenerated (Submodule R M) :=
   ⟨fun s =>
     ⟨(fun x => span R {x}) '' s,
       ⟨fun t ht => by
-        rcases(Set.mem_image _ _ _).1 ht with ⟨x, _, rfl⟩
+        rcases (Set.mem_image _ _ _).1 ht with ⟨x, _, rfl⟩
         apply singleton_span_isCompactElement, by
         rw [sSup_eq_iSup, iSup_image, ← span_eq_iSup_of_singleton_spans, span_eq]⟩⟩⟩
 

They key addition is the lemma LieAlgebra.IsKilling.ker_restrictBilinear_of_isCartanSubalgebra_eq_bot.

@@ -373,6 +373,11 @@ theorem mem_sup' : x ∈ p ⊔ p' ↔ ∃ (y : p) (z : p'), (y : M) + z = x :=
   mem_sup.trans <| by simp only [Subtype.exists, exists_prop]
 #align submodule.mem_sup' Submodule.mem_sup'
 
+lemma exists_add_eq_of_codisjoint (h : Codisjoint p p') (x : M) :
+    ∃ y ∈ p, ∃ z ∈ p', y + z = x := by
+  suffices x ∈ p ⊔ p' by exact Submodule.mem_sup.mp this
+  simpa only [h.eq_top] using Submodule.mem_top
+
 variable (p p')
 
 theorem coe_sup : ↑(p ⊔ p') = (p + p' : Set M) := by

The point is that the following four lemmas are now all true by definition:

• LieSubmodule.inf_coe_toSubmodule
• LieSubmodule.sInf_coe_toSubmodule
• LieSubmodule.sup_coe_toSubmodule [previously existed but not true by definition]
• LieSubmodule.sSup_coe_toSubmodule [previously did not exist]

@@ -706,6 +706,10 @@ theorem mem_iSup {ι : Sort*} (p : ι → Submodule R M) {m : M} :
   simp only [span_singleton_le_iff_mem]
 #align submodule.mem_supr Submodule.mem_iSup
 
+theorem mem_sSup {s : Set (Submodule R M)} {m : M} :
+    (m ∈ sSup s) ↔ ∀ N, (∀ p ∈ s, p ≤ N) → m ∈ N := by
+  simp_rw [sSup_eq_iSup, Submodule.mem_iSup, iSup_le_iff]
+
 section
 
 /-- For every element in the span of a set, there exists a finite subset of the set

And fix some names in comments where this revealed issues

@@ -292,7 +292,7 @@ theorem subset_span_trans {U V W : Set M} (hUV : U ⊆ Submodule.span R V)
   (Submodule.gi R M).gc.le_u_l_trans hUV hVW
 #align submodule.subset_span_trans Submodule.subset_span_trans
 
-/-- See `submodule.span_smul_eq` (in `RingTheory.Ideal.Operations`) for
+/-- See `Submodule.span_smul_eq` (in `RingTheory.Ideal.Operations`) for
 `span R (r • s) = r • span R s` that holds for arbitrary `r` in a `CommSemiring`. -/
 theorem span_smul_eq_of_isUnit (s : Set M) (r : R) (hr : IsUnit r) : span R (r • s) = span R s := by
   apply le_antisymm

To check that a property is true ae in a vector space, it suffices to check that it is true ae along all translates of a given vector subspace.

@@ -839,6 +839,29 @@ theorem comap_map_eq_self {f : F} {p : Submodule R M} (h : LinearMap.ker f ≤ p
     comap f (map f p) = p := by rw [Submodule.comap_map_eq, sup_of_le_left h]
 #align submodule.comap_map_eq_self Submodule.comap_map_eq_self
 
+lemma _root_.LinearMap.range_domRestrict_eq_range_iff {f : M →ₛₗ[τ₁₂] M₂} {S : Submodule R M} :
+    LinearMap.range (f.domRestrict S) = LinearMap.range f ↔ S ⊔ (LinearMap.ker f) = ⊤ := by
+  refine ⟨fun h ↦ ?_, fun h ↦ ?_⟩
+  · rw [eq_top_iff]
+    intro x _
+    have : f x ∈ LinearMap.range f := LinearMap.mem_range_self f x
+    rw [← h] at this
+    obtain ⟨y, hy⟩ : ∃ y : S, f.domRestrict S y = f x := this
+    have : (y : M) + (x - y) ∈ S ⊔ (LinearMap.ker f) := Submodule.add_mem_sup y.2 (by simp [← hy])
+    simpa using this
+  · refine le_antisymm (LinearMap.range_domRestrict_le_range f S) ?_
+    rintro x ⟨y, rfl⟩
+    obtain ⟨s, hs, t, ht, rfl⟩ : ∃ s, s ∈ S ∧ ∃ t, t ∈ LinearMap.ker f ∧ s + t = y :=
+      Submodule.mem_sup.1 (by simp [h])
+    exact ⟨⟨s, hs⟩, by simp [LinearMap.mem_ker.1 ht]⟩
+
+@[simp] lemma _root_.LinearMap.surjective_domRestrict_iff
+    {f : M →ₛₗ[τ₁₂] M₂} {S : Submodule R M} (hf : Surjective f) :
+    Surjective (f.domRestrict S) ↔ S ⊔ LinearMap.ker f = ⊤ := by
+  rw [← LinearMap.range_eq_top] at hf ⊢
+  rw [← hf]
+  exact LinearMap.range_domRestrict_eq_range_iff
+
 end AddCommGroup
 
 section DivisionRing

Also add supporting lemmas and golf some proofs.

Based on a file from the Sphere Eversion Project.

@@ -484,20 +484,7 @@ theorem mem_span_singleton_trans {x y z : M} (hxy : x ∈ R ∙ y) (hyz : y ∈
   exact Submodule.subset_span_trans hxy hyz
 #align submodule.mem_span_singleton_trans Submodule.mem_span_singleton_trans
 
-theorem mem_span_insert {y} :
-    x ∈ span R (insert y s) ↔ ∃ a : R, ∃ z ∈ span R s, x = a • y + z := by
-  simp only [← union_singleton, span_union, mem_sup, mem_span_singleton, exists_prop,
-    exists_exists_eq_and]
-  rw [exists_comm]
-  simp only [eq_comm, add_comm, exists_and_left]
-#align submodule.mem_span_insert Submodule.mem_span_insert
-
-theorem mem_span_pair {x y z : M} :
-    z ∈ span R ({x, y} : Set M) ↔ ∃ a b : R, a • x + b • y = z := by
-  simp_rw [mem_span_insert, mem_span_singleton, exists_exists_eq_and, eq_comm]
-#align submodule.mem_span_pair Submodule.mem_span_pair
-
-theorem span_insert (x) (s : Set M) : span R (insert x s) = span R ({x} : Set M) ⊔ span R s := by
+theorem span_insert (x) (s : Set M) : span R (insert x s) = (R ∙ x) ⊔ span R s := by
   rw [insert_eq, span_union]
 #align submodule.span_insert Submodule.span_insert
 
@@ -509,6 +496,16 @@ theorem span_span : span R (span R s : Set M) = span R s :=
   span_eq _
 #align submodule.span_span Submodule.span_span
 
+theorem mem_span_insert {y} :
+    x ∈ span R (insert y s) ↔ ∃ a : R, ∃ z ∈ span R s, x = a • y + z := by
+  simp [span_insert, mem_sup, mem_span_singleton, eq_comm (a := x)]
+#align submodule.mem_span_insert Submodule.mem_span_insert
+
+theorem mem_span_pair {x y z : M} :
+    z ∈ span R ({x, y} : Set M) ↔ ∃ a b : R, a • x + b • y = z := by
+  simp_rw [mem_span_insert, mem_span_singleton, exists_exists_eq_and, eq_comm]
+#align submodule.mem_span_pair Submodule.mem_span_pair
+
 variable (R S s)
 
 /-- If `R` is "smaller" ring than `S` then the span by `R` is smaller than the span by `S`. -/
@@ -548,37 +545,25 @@ theorem span_singleton_eq_bot : (R ∙ x) = ⊥ ↔ x = 0 :=
 theorem span_zero : span R (0 : Set M) = ⊥ := by rw [← singleton_zero, span_singleton_eq_bot]
 #align submodule.span_zero Submodule.span_zero
 
+@[simp]
+theorem span_singleton_le_iff_mem (m : M) (p : Submodule R M) : (R ∙ m) ≤ p ↔ m ∈ p := by
+  rw [span_le, singleton_subset_iff, SetLike.mem_coe]
+#align submodule.span_singleton_le_iff_mem Submodule.span_singleton_le_iff_mem
+
 theorem span_singleton_eq_span_singleton {R M : Type*} [Ring R] [AddCommGroup M] [Module R M]
     [NoZeroSMulDivisors R M] {x y : M} : ((R ∙ x) = R ∙ y) ↔ ∃ z : Rˣ, z • x = y := by
-  by_cases hx : x = 0
-  · rw [hx, span_zero_singleton, eq_comm, span_singleton_eq_bot]
-    exact ⟨fun hy => ⟨1, by rw [hy, smul_zero]⟩, fun ⟨_, hz⟩ => by rw [← hz, smul_zero]⟩
-  by_cases hy : y = 0
-  · rw [hy, span_zero_singleton, span_singleton_eq_bot]
-    exact ⟨fun hx => ⟨1, by rw [hx, smul_zero]⟩, fun ⟨z, hz⟩ => (smul_eq_zero_iff_eq z).mp hz⟩
   constructor
-  · intro hxy
-    cases'
-      mem_span_singleton.mp
-        (by
-          rw [hxy]
-          apply mem_span_singleton_self) with
-      v hv
-    cases'
-      mem_span_singleton.mp
-        (by
-          rw [← hxy]
-          apply mem_span_singleton_self) with
-      i hi
-    have vi : v * i = 1 := by
-      rw [← one_smul R y, ← hi, smul_smul] at hv
-      exact smul_left_injective R hy hv
-    have iv : i * v = 1 := by
-      rw [← one_smul R x, ← hv, smul_smul] at hi
-      exact smul_left_injective R hx hi
-    exact ⟨⟨v, i, vi, iv⟩, hv⟩
-  · rintro ⟨v, rfl⟩
-    rw [span_singleton_group_smul_eq]
+  · simp only [le_antisymm_iff, span_singleton_le_iff_mem, mem_span_singleton]
+    rintro ⟨⟨a, rfl⟩, b, hb⟩
+    rcases eq_or_ne y 0 with rfl | hy; · simp
+    refine ⟨⟨b, a, ?_, ?_⟩, hb⟩
+    · apply smul_left_injective R hy
+      simpa only [mul_smul, one_smul]
+    · rw [← hb] at hy
+      apply smul_left_injective R (smul_ne_zero_iff.1 hy).2
+      simp only [mul_smul, one_smul, hb]
+  · rintro ⟨u, rfl⟩
+    exact (span_singleton_group_smul_eq _ _ _).symm
 #align submodule.span_singleton_eq_span_singleton Submodule.span_singleton_eq_span_singleton
 
 @[simp]
@@ -664,11 +649,6 @@ theorem iSup_induction' {ι : Sort*} (p : ι → Submodule R M) {C : ∀ x, (x 
     refine' ⟨_, hadd _ _ _ _ Cx Cy⟩
 #align submodule.supr_induction' Submodule.iSup_induction'
 
-@[simp]
-theorem span_singleton_le_iff_mem (m : M) (p : Submodule R M) : (R ∙ m) ≤ p ↔ m ∈ p := by
-  rw [span_le, singleton_subset_iff, SetLike.mem_coe]
-#align submodule.span_singleton_le_iff_mem Submodule.span_singleton_le_iff_mem
-
 theorem singleton_span_isCompactElement (x : M) :
     CompleteLattice.IsCompactElement (span R {x} : Submodule R M) := by
   rw [CompleteLattice.isCompactElement_iff_le_of_directed_sSup_le]
@@ -717,27 +697,7 @@ theorem submodule_eq_sSup_le_nonzero_spans (p : Submodule R M) :
     rwa [span_singleton_le_iff_mem]
 #align submodule.submodule_eq_Sup_le_nonzero_spans Submodule.submodule_eq_sSup_le_nonzero_spans
 
-theorem lt_sup_iff_not_mem {I : Submodule R M} {a : M} : (I < I ⊔ R ∙ a) ↔ a ∉ I := by
-  constructor
-  · intro h
-    by_contra akey
-    have h1 : (I ⊔ R ∙ a) ≤ I := by
-      simp only [sup_le_iff]
-      constructor
-      · exact le_refl I
-      · exact (span_singleton_le_iff_mem a I).mpr akey
-    have h2 := gt_of_ge_of_gt h1 h
-    exact lt_irrefl I h2
-  · intro h
-    apply SetLike.lt_iff_le_and_exists.mpr
-    constructor
-    simp only [le_sup_left]
-    use a
-    constructor
-    swap
-    · assumption
-    · have : (R ∙ a) ≤ I ⊔ R ∙ a := le_sup_right
-      exact this (mem_span_singleton_self a)
+theorem lt_sup_iff_not_mem {I : Submodule R M} {a : M} : (I < I ⊔ R ∙ a) ↔ a ∉ I := by simp
 #align submodule.lt_sup_iff_not_mem Submodule.lt_sup_iff_not_mem
 
 theorem mem_iSup {ι : Sort*} (p : ι → Submodule R M) {m : M} :
@@ -881,6 +841,28 @@ theorem comap_map_eq_self {f : F} {p : Submodule R M} (h : LinearMap.ker f ≤ p
 
 end AddCommGroup
 
+section DivisionRing
+
+variable [DivisionRing K] [AddCommGroup V] [Module K V]
+
+/-- There is no vector subspace between `p` and `(K ∙ x) ⊔ p`, `Wcovby` version. -/
+theorem wcovby_span_singleton_sup (x : V) (p : Submodule K V) : Wcovby p ((K ∙ x) ⊔ p) := by
+  refine ⟨le_sup_right, fun q hpq hqp ↦ hqp.not_le ?_⟩
+  rcases SetLike.exists_of_lt hpq with ⟨y, hyq, hyp⟩
+  obtain ⟨c, z, hz, rfl⟩ : ∃ c : K, ∃ z ∈ p, c • x + z = y := by
+    simpa [mem_sup, mem_span_singleton] using hqp.le hyq
+  rcases eq_or_ne c 0 with rfl | hc
+  · simp [hz] at hyp
+  · have : x ∈ q
+    · rwa [q.add_mem_iff_left (hpq.le hz), q.smul_mem_iff hc] at hyq
+    simp [hpq.le, this]
+
+/-- There is no vector subspace between `p` and `(K ∙ x) ⊔ p`, `Covby` version. -/
+theorem covby_span_singleton_sup {x : V} {p : Submodule K V} (h : x ∉ p) : Covby p ((K ∙ x) ⊔ p) :=
+  ⟨by simpa, (wcovby_span_singleton_sup _ _).2⟩
+
+end DivisionRing
+
 end Submodule
 
 namespace LinearMap
@@ -1010,13 +992,10 @@ variable [Field K] [AddCommGroup V] [Module K V]
 
 theorem span_singleton_sup_ker_eq_top (f : V →ₗ[K] K) {x : V} (hx : f x ≠ 0) :
     (K ∙ x) ⊔ ker f = ⊤ :=
-  eq_top_iff.2 fun y _ =>
+  top_unique fun y _ =>
     Submodule.mem_sup.2
       ⟨(f y * (f x)⁻¹) • x, Submodule.mem_span_singleton.2 ⟨f y * (f x)⁻¹, rfl⟩,
-        ⟨y - (f y * (f x)⁻¹) • x, by
-          rw [LinearMap.mem_ker, f.map_sub, f.map_smul, smul_eq_mul, mul_assoc, inv_mul_cancel hx,
-            mul_one, sub_self],
-          by simp only [add_sub_cancel'_right]⟩⟩
+        ⟨y - (f y * (f x)⁻¹) • x, by simp [hx]⟩⟩
 #align linear_map.span_singleton_sup_ker_eq_top LinearMap.span_singleton_sup_ker_eq_top
 
 end Field

In Mathlib/LinearAlgebra/Dual.lean we also overhaul the universe argument names, as the file switched between two conventions and making up undeclared universe variables.

Mathlib/LinearAlgebra/Prod.lean invented some new variables even though it already had plenty available.

@@ -23,9 +23,6 @@ import Mathlib.Tactic.Ring
 
 -/
 
-set_option autoImplicit true
-
-
 variable {R R₂ K M M₂ V S : Type*}
 
 namespace Submodule
@@ -155,7 +152,7 @@ theorem span_induction {p : M → Prop} (h : x ∈ span R s) (Hs : ∀ x ∈ s,
 
 /-- An induction principle for span membership. This is a version of `Submodule.span_induction`
 for binary predicates. -/
-theorem span_induction₂ {p : M → M → Prop} (ha : a ∈ Submodule.span R s)
+theorem span_induction₂ {p : M → M → Prop} {a b : M} (ha : a ∈ Submodule.span R s)
     (hb : b ∈ Submodule.span R s) (Hs : ∀ x ∈ s, ∀ y ∈ s, p x y)
     (H0_left : ∀ y, p 0 y) (H0_right : ∀ x, p x 0)
     (Hadd_left : ∀ x₁ x₂ y, p x₁ y → p x₂ y → p (x₁ + x₂) y)

@@ -101,7 +101,7 @@ theorem map_span [RingHomSurjective σ₁₂] (f : F) (s : Set M) :
       map_le_iff_le_comap.2 <| span_le.2 fun x hx => subset_span ⟨x, hx, rfl⟩
 #align submodule.map_span Submodule.map_span
 
-alias Submodule.map_span ← _root_.LinearMap.map_span
+alias _root_.LinearMap.map_span := Submodule.map_span
 #align linear_map.map_span LinearMap.map_span
 
 theorem map_span_le [RingHomSurjective σ₁₂] (f : F) (s : Set M) (N : Submodule R₂ M₂) :
@@ -110,7 +110,7 @@ theorem map_span_le [RingHomSurjective σ₁₂] (f : F) (s : Set M) (N : Submod
   exact Iff.rfl
 #align submodule.map_span_le Submodule.map_span_le
 
-alias Submodule.map_span_le ← _root_.LinearMap.map_span_le
+alias _root_.LinearMap.map_span_le := Submodule.map_span_le
 #align linear_map.map_span_le LinearMap.map_span_le
 
 @[simp]
@@ -127,7 +127,7 @@ theorem span_preimage_le (f : F) (s : Set M₂) :
   exact preimage_mono subset_span
 #align submodule.span_preimage_le Submodule.span_preimage_le
 
-alias Submodule.span_preimage_le ← _root_.LinearMap.span_preimage_le
+alias _root_.LinearMap.span_preimage_le := Submodule.span_preimage_le
 #align linear_map.span_preimage_le LinearMap.span_preimage_le
 
 theorem closure_subset_span {s : Set M} : (AddSubmonoid.closure s : Set M) ⊆ span R s :=

The main difficulty here is that * has a slightly difference precedence to ⬝. notably around smul and neg.

The other annoyance is that ↑U ⬝ A ⬝ ↑U⁻¹ : Matrix m m 𝔸 now has to be written U.val * A * (U⁻¹).val in order to typecheck.

A downside of this change to consider: if you have a goal of A * (B * C) = (A * B) * C, mul_assoc now gives the illusion of matching, when in fact Matrix.mul_assoc is needed. Previously the distinct symbol made it easy to avoid this mistake.

On the flipside, there is now no need to rewrite by Matrix.mul_eq_mul all the time (indeed, the lemma is now removed).

@@ -273,7 +273,7 @@ theorem span_sup : span R s ⊔ p = span R (s ∪ p) := by rw [Submodule.span_un
 -- mathport name: «expr ∙ »
 notation:1000
   /- Note that the character `∙` U+2219 used below is different from the scalar multiplication
-character `•` U+2022 and the matrix multiplication character `⬝` U+2B1D. -/
+character `•` U+2022. -/
 R " ∙ " x => span R (singleton x)
 
 theorem span_eq_iSup_of_singleton_spans (s : Set M) : span R s = ⨆ x ∈ s, R ∙ x := by

Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.

The intent of this PR is to make autoImplicit opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true in the few files that rely on it.

That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.

I claim that many of the uses of autoImplicit in these files are accidental; situations such as:

• Assuming variables are in scope, but pasting the lemma in the wrong section
• Pasting in a lemma from a scratch file without checking to see if the variable names are consistent with the rest of the file
• Making a copy-paste error between lemmas and forgetting to add an explicit arguments.

Having set_option autoImplicit false as the default prevents these types of mistake being made in the 90% of files where autoImplicits are not used at all, and causes them to be caught by CI during review.

I think there were various points during the port where we encouraged porters to delete the universes u v lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.

A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18 as the no:dontcare:yes vote ratio.

While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true has been placed locally within a section, rather than at the top of the file.

@@ -23,6 +23,8 @@ import Mathlib.Tactic.Ring
 
 -/
 
+set_option autoImplicit true
+
 
 variable {R R₂ K M M₂ V S : Type*}
 

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

This has nice performance benefits.

@@ -24,7 +24,7 @@ import Mathlib.Tactic.Ring
 -/
 
 
-variable {R R₂ K M M₂ V S : Type _}
+variable {R R₂ K M M₂ V S : Type*}
 
 namespace Submodule
 
@@ -40,7 +40,7 @@ variable {x : M} (p p' : Submodule R M)
 
 variable [Semiring R₂] {σ₁₂ : R →+* R₂}
 
-variable [AddCommMonoid M₂] [Module R₂ M₂] {F : Type _} [SemilinearMapClass F σ₁₂ M M₂]
+variable [AddCommMonoid M₂] [Module R₂ M₂] {F : Type*} [SemilinearMapClass F σ₁₂ M M₂]
 
 section
 
@@ -205,7 +205,7 @@ theorem span_nat_eq (s : AddSubmonoid M) : (span ℕ (s : Set M)).toAddSubmonoid
   rw [span_nat_eq_addSubmonoid_closure, s.closure_eq]
 #align submodule.span_nat_eq Submodule.span_nat_eq
 
-theorem span_int_eq_addSubgroup_closure {M : Type _} [AddCommGroup M] (s : Set M) :
+theorem span_int_eq_addSubgroup_closure {M : Type*} [AddCommGroup M] (s : Set M) :
     (span ℤ s).toAddSubgroup = AddSubgroup.closure s :=
   Eq.symm <|
     AddSubgroup.closure_eq_of_le _ subset_span fun x hx =>
@@ -214,7 +214,7 @@ theorem span_int_eq_addSubgroup_closure {M : Type _} [AddCommGroup M] (s : Set M
 #align submodule.span_int_eq_add_subgroup_closure Submodule.span_int_eq_addSubgroup_closure
 
 @[simp]
-theorem span_int_eq {M : Type _} [AddCommGroup M] (s : AddSubgroup M) :
+theorem span_int_eq {M : Type*} [AddCommGroup M] (s : AddSubgroup M) :
     (span ℤ (s : Set M)).toAddSubgroup = s := by rw [span_int_eq_addSubgroup_closure, s.closure_eq]
 #align submodule.span_int_eq Submodule.span_int_eq
 
@@ -253,12 +253,12 @@ theorem span_iUnion {ι} (s : ι → Set M) : span R (⋃ i, s i) = ⨆ i, span
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem span_iUnion₂ {ι} {κ : ι → Sort _} (s : ∀ i, κ i → Set M) :
+theorem span_iUnion₂ {ι} {κ : ι → Sort*} (s : ∀ i, κ i → Set M) :
     span R (⋃ (i) (j), s i j) = ⨆ (i) (j), span R (s i j) :=
   (Submodule.gi R M).gc.l_iSup₂
 #align submodule.span_Union₂ Submodule.span_iUnion₂
 
-theorem span_attach_biUnion [DecidableEq M] {α : Type _} (s : Finset α) (f : s → Finset M) :
+theorem span_attach_biUnion [DecidableEq M] {α : Type*} (s : Finset α) (f : s → Finset M) :
     span R (s.attach.biUnion f : Set M) = ⨆ x, span R (f x) := by simp [span_iUnion]
 #align submodule.span_attach_bUnion Submodule.span_attach_biUnion
 
@@ -278,7 +278,7 @@ theorem span_eq_iSup_of_singleton_spans (s : Set M) : span R s = ⨆ x ∈ s, R
   simp only [← span_iUnion, Set.biUnion_of_singleton s]
 #align submodule.span_eq_supr_of_singleton_spans Submodule.span_eq_iSup_of_singleton_spans
 
-theorem span_range_eq_iSup {ι : Type _} {v : ι → M} : span R (range v) = ⨆ i, R ∙ v i := by
+theorem span_range_eq_iSup {ι : Type*} {v : ι → M} : span R (range v) = ⨆ i, R ∙ v i := by
   rw [span_eq_iSup_of_singleton_spans, iSup_range]
 #align submodule.span_range_eq_supr Submodule.span_range_eq_iSup
 
@@ -388,7 +388,7 @@ theorem sup_toAddSubmonoid : (p ⊔ p').toAddSubmonoid = p.toAddSubmonoid ⊔ p'
   rfl
 #align submodule.sup_to_add_submonoid Submodule.sup_toAddSubmonoid
 
-theorem sup_toAddSubgroup {R M : Type _} [Ring R] [AddCommGroup M] [Module R M]
+theorem sup_toAddSubgroup {R M : Type*} [Ring R] [AddCommGroup M] [Module R M]
     (p p' : Submodule R M) : (p ⊔ p').toAddSubgroup = p.toAddSubgroup ⊔ p'.toAddSubgroup := by
   ext x
   rw [mem_toAddSubgroup, mem_sup, AddSubgroup.mem_sup]
@@ -464,7 +464,7 @@ theorem span_singleton_smul_eq {r : R} (hr : IsUnit r) (x : M) : (R ∙ r • x)
   exact span_singleton_group_smul_eq R r x
 #align submodule.span_singleton_smul_eq Submodule.span_singleton_smul_eq
 
-theorem disjoint_span_singleton {K E : Type _} [DivisionRing K] [AddCommGroup E] [Module K E]
+theorem disjoint_span_singleton {K E : Type*} [DivisionRing K] [AddCommGroup E] [Module K E]
     {s : Submodule K E} {x : E} : Disjoint s (K ∙ x) ↔ x ∈ s → x = 0 := by
   refine' disjoint_def.trans ⟨fun H hx => H x hx <| subset_span <| mem_singleton x, _⟩
   intro H y hy hyx
@@ -475,7 +475,7 @@ theorem disjoint_span_singleton {K E : Type _} [DivisionRing K] [AddCommGroup E]
     rw [H hy, smul_zero]
 #align submodule.disjoint_span_singleton Submodule.disjoint_span_singleton
 
-theorem disjoint_span_singleton' {K E : Type _} [DivisionRing K] [AddCommGroup E] [Module K E]
+theorem disjoint_span_singleton' {K E : Type*} [DivisionRing K] [AddCommGroup E] [Module K E]
     {p : Submodule K E} {x : E} (x0 : x ≠ 0) : Disjoint p (K ∙ x) ↔ x ∉ p :=
   disjoint_span_singleton.trans ⟨fun h₁ h₂ => x0 (h₁ h₂), fun h₁ h₂ => (h₁ h₂).elim⟩
 #align submodule.disjoint_span_singleton' Submodule.disjoint_span_singleton'
@@ -549,7 +549,7 @@ theorem span_singleton_eq_bot : (R ∙ x) = ⊥ ↔ x = 0 :=
 theorem span_zero : span R (0 : Set M) = ⊥ := by rw [← singleton_zero, span_singleton_eq_bot]
 #align submodule.span_zero Submodule.span_zero
 
-theorem span_singleton_eq_span_singleton {R M : Type _} [Ring R] [AddCommGroup M] [Module R M]
+theorem span_singleton_eq_span_singleton {R M : Type*} [Ring R] [AddCommGroup M] [Module R M]
     [NoZeroSMulDivisors R M] {x y : M} : ((R ∙ x) = R ∙ y) ↔ ∃ z : Rˣ, z • x = y := by
   by_cases hx : x = 0
   · rw [hx, span_zero_singleton, eq_comm, span_singleton_eq_bot]
@@ -610,16 +610,16 @@ theorem not_mem_span_of_apply_not_mem_span_image [RingHomSurjective σ₁₂] (f
   h.imp (apply_mem_span_image_of_mem_span f)
 #align submodule.not_mem_span_of_apply_not_mem_span_image Submodule.not_mem_span_of_apply_not_mem_span_image
 
-theorem iSup_span {ι : Sort _} (p : ι → Set M) : ⨆ i, span R (p i) = span R (⋃ i, p i) :=
+theorem iSup_span {ι : Sort*} (p : ι → Set M) : ⨆ i, span R (p i) = span R (⋃ i, p i) :=
   le_antisymm (iSup_le fun i => span_mono <| subset_iUnion _ i) <|
     span_le.mpr <| iUnion_subset fun i _ hm => mem_iSup_of_mem i <| subset_span hm
 #align submodule.supr_span Submodule.iSup_span
 
-theorem iSup_eq_span {ι : Sort _} (p : ι → Submodule R M) : ⨆ i, p i = span R (⋃ i, ↑(p i)) := by
+theorem iSup_eq_span {ι : Sort*} (p : ι → Submodule R M) : ⨆ i, p i = span R (⋃ i, ↑(p i)) := by
   simp_rw [← iSup_span, span_eq]
 #align submodule.supr_eq_span Submodule.iSup_eq_span
 
-theorem iSup_toAddSubmonoid {ι : Sort _} (p : ι → Submodule R M) :
+theorem iSup_toAddSubmonoid {ι : Sort*} (p : ι → Submodule R M) :
     (⨆ i, p i).toAddSubmonoid = ⨆ i, (p i).toAddSubmonoid := by
   refine' le_antisymm (fun x => _) (iSup_le fun i => toAddSubmonoid_mono <| le_iSup _ i)
   simp_rw [iSup_eq_span, AddSubmonoid.iSup_eq_closure, mem_toAddSubmonoid, coe_toAddSubmonoid]
@@ -643,7 +643,7 @@ theorem iSup_toAddSubmonoid {ι : Sort _} (p : ι → Submodule R M) :
 If `C` holds for `0` and all elements of `p i` for all `i`, and is preserved under addition,
 then it holds for all elements of the supremum of `p`. -/
 @[elab_as_elim]
-theorem iSup_induction {ι : Sort _} (p : ι → Submodule R M) {C : M → Prop} {x : M}
+theorem iSup_induction {ι : Sort*} (p : ι → Submodule R M) {C : M → Prop} {x : M}
     (hx : x ∈ ⨆ i, p i) (hp : ∀ (i), ∀ x ∈ p i, C x) (h0 : C 0)
     (hadd : ∀ x y, C x → C y → C (x + y)) : C x := by
   rw [← mem_toAddSubmonoid, iSup_toAddSubmonoid] at hx
@@ -652,7 +652,7 @@ theorem iSup_induction {ι : Sort _} (p : ι → Submodule R M) {C : M → Prop}
 
 /-- A dependent version of `submodule.iSup_induction`. -/
 @[elab_as_elim]
-theorem iSup_induction' {ι : Sort _} (p : ι → Submodule R M) {C : ∀ x, (x ∈ ⨆ i, p i) → Prop}
+theorem iSup_induction' {ι : Sort*} (p : ι → Submodule R M) {C : ∀ x, (x ∈ ⨆ i, p i) → Prop}
     (hp : ∀ (i) (x) (hx : x ∈ p i), C x (mem_iSup_of_mem i hx)) (h0 : C 0 (zero_mem _))
     (hadd : ∀ x y hx hy, C x hx → C y hy → C (x + y) (add_mem ‹_› ‹_›)) {x : M}
     (hx : x ∈ ⨆ i, p i) : C x hx := by
@@ -741,7 +741,7 @@ theorem lt_sup_iff_not_mem {I : Submodule R M} {a : M} : (I < I ⊔ R ∙ a) ↔
       exact this (mem_span_singleton_self a)
 #align submodule.lt_sup_iff_not_mem Submodule.lt_sup_iff_not_mem
 
-theorem mem_iSup {ι : Sort _} (p : ι → Submodule R M) {m : M} :
+theorem mem_iSup {ι : Sort*} (p : ι → Submodule R M) {m : M} :
     (m ∈ ⨆ i, p i) ↔ ∀ N, (∀ i, p i ≤ N) → m ∈ N := by
   rw [← span_singleton_le_iff_mem, le_iSup_iff]
   simp only [span_singleton_le_iff_mem]
@@ -773,7 +773,7 @@ theorem mem_span_finite_of_mem_span {S : Set M} {x : M} (hx : x ∈ span R S) :
 
 end
 
-variable {M' : Type _} [AddCommMonoid M'] [Module R M'] (q₁ q₁' : Submodule R M')
+variable {M' : Type*} [AddCommMonoid M'] [Module R M'] (q₁ q₁' : Submodule R M')
 
 /-- The product of two submodules is a submodule. -/
 def prod : Submodule R (M × M') :=
@@ -868,7 +868,7 @@ variable [AddCommGroup M] [Module R M] [AddCommGroup M₂] [Module R₂ M₂]
 
 variable {τ₁₂ : R →+* R₂} [RingHomSurjective τ₁₂]
 
-variable {F : Type _} [sc : SemilinearMapClass F τ₁₂ M M₂]
+variable {F : Type*} [sc : SemilinearMapClass F τ₁₂ M M₂]
 
 theorem comap_map_eq (f : F) (p : Submodule R M) : comap f (map f p) = p ⊔ LinearMap.ker f := by
   refine' le_antisymm _ (sup_le (le_comap_map _ _) (comap_mono bot_le))
@@ -898,7 +898,7 @@ variable [Module R M] [Module R₂ M₂]
 
 variable {τ₁₂ : R →+* R₂} [RingHomSurjective τ₁₂]
 
-variable {F : Type _} [sc : SemilinearMapClass F τ₁₂ M M₂]
+variable {F : Type*} [sc : SemilinearMapClass F τ₁₂ M M₂]
 
 protected theorem map_le_map_iff (f : F) {p p'} : map f p ≤ map f p' ↔ p ≤ p' ⊔ ker f := by
   rw [map_le_iff_le_comap, Submodule.comap_map_eq]
@@ -956,7 +956,7 @@ variable [Semiring R] [AddCommMonoid M] [Module R M]
 
 variable [Semiring R₂] [AddCommMonoid M₂] [Module R₂ M₂]
 
-variable {F : Type _} {σ₁₂ : R →+* R₂} [SemilinearMapClass F σ₁₂ M M₂]
+variable {F : Type*} {σ₁₂ : R →+* R₂} [SemilinearMapClass F σ₁₂ M M₂]
 
 /-- Two linear maps are equal on `Submodule.span s` iff they are equal on `s`. -/
 theorem eqOn_span_iff {s : Set M} {f g : F} : Set.EqOn f g (span R s) ↔ Set.EqOn f g s := by
@@ -987,7 +987,7 @@ theorem ext_on {s : Set M} {f g : F} (hv : span R s = ⊤) (h : Set.EqOn f g s)
 
 /-- If the range of `v : ι → M` generates the whole module and linear maps `f`, `g` are equal at
 each `v i`, then they are equal. -/
-theorem ext_on_range {ι : Type _} {v : ι → M} {f g : F} (hv : span R (Set.range v) = ⊤)
+theorem ext_on_range {ι : Type*} {v : ι → M} {f g : F} (hv : span R (Set.range v) = ⊤)
     (h : ∀ i, f (v i) = g (v i)) : f = g :=
   ext_on hv (Set.forall_range_iff.2 h)
 #align linear_map.ext_on_range LinearMap.ext_on_range

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.

@@ -749,12 +749,11 @@ theorem mem_iSup {ι : Sort _} (p : ι → Submodule R M) {m : M} :
 
 section
 
-open Classical
-
 /-- For every element in the span of a set, there exists a finite subset of the set
 such that the element is contained in the span of the subset. -/
 theorem mem_span_finite_of_mem_span {S : Set M} {x : M} (hx : x ∈ span R S) :
     ∃ T : Finset M, ↑T ⊆ S ∧ x ∈ span R (T : Set M) := by
+  classical
   refine' span_induction hx (fun x hx => _) _ _ _
   · refine' ⟨{x}, _, _⟩
     · rwa [Finset.coe_singleton, Set.singleton_subset_iff]
@@ -1010,8 +1009,6 @@ section Field
 
 variable [Field K] [AddCommGroup V] [Module K V]
 
-open Classical
-
 theorem span_singleton_sup_ker_eq_top (f : V →ₗ[K] K) {x : V} (hx : f x ≠ 0) :
     (K ∙ x) ⊔ ker f = ⊤ :=
   eq_top_iff.2 fun y _ =>

Add the following result:

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

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

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

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

@@ -40,7 +40,7 @@ variable {x : M} (p p' : Submodule R M)
 
 variable [Semiring R₂] {σ₁₂ : R →+* R₂}
 
-variable [AddCommMonoid M₂] [Module R₂ M₂]
+variable [AddCommMonoid M₂] [Module R₂ M₂] {F : Type _} [SemilinearMapClass F σ₁₂ M M₂]
 
 section
 
@@ -92,7 +92,7 @@ theorem span_coe_eq_restrictScalars [Semiring S] [SMul S R] [Module S M] [IsScal
   span_eq (p.restrictScalars S)
 #align submodule.span_coe_eq_restrict_scalars Submodule.span_coe_eq_restrictScalars
 
-theorem map_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (s : Set M) :
+theorem map_span [RingHomSurjective σ₁₂] (f : F) (s : Set M) :
     (span R s).map f = span R₂ (f '' s) :=
   Eq.symm <|
     span_eq_of_le _ (Set.image_subset f subset_span) <|
@@ -102,9 +102,9 @@ theorem map_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (
 alias Submodule.map_span ← _root_.LinearMap.map_span
 #align linear_map.map_span LinearMap.map_span
 
-theorem map_span_le [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) (s : Set M) (N : Submodule R₂ M₂) :
+theorem map_span_le [RingHomSurjective σ₁₂] (f : F) (s : Set M) (N : Submodule R₂ M₂) :
     map f (span R s) ≤ N ↔ ∀ m ∈ s, f m ∈ N := by
-  rw [f.map_span, span_le, Set.image_subset_iff]
+  rw [map_span, span_le, Set.image_subset_iff]
   exact Iff.rfl
 #align submodule.map_span_le Submodule.map_span_le
 
@@ -119,7 +119,7 @@ theorem span_insert_zero : span R (insert (0 : M) s) = span R s := by
 #align submodule.span_insert_zero Submodule.span_insert_zero
 
 -- See also `span_preimage_eq` below.
-theorem span_preimage_le (f : M →ₛₗ[σ₁₂] M₂) (s : Set M₂) :
+theorem span_preimage_le (f : F) (s : Set M₂) :
     span R (f ⁻¹' s) ≤ (span R₂ s).comap f := by
   rw [span_le, comap_coe]
   exact preimage_mono subset_span
@@ -583,18 +583,18 @@ theorem span_singleton_eq_span_singleton {R M : Type _} [Ring R] [AddCommGroup M
 #align submodule.span_singleton_eq_span_singleton Submodule.span_singleton_eq_span_singleton
 
 @[simp]
-theorem span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) :
+theorem span_image [RingHomSurjective σ₁₂] (f : F) :
     span R₂ (f '' s) = map f (span R s) :=
   (map_span f s).symm
 #align submodule.span_image Submodule.span_image
 
-theorem apply_mem_span_image_of_mem_span [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) {x : M}
+theorem apply_mem_span_image_of_mem_span [RingHomSurjective σ₁₂] (f : F) {x : M}
     {s : Set M} (h : x ∈ Submodule.span R s) : f x ∈ Submodule.span R₂ (f '' s) := by
   rw [Submodule.span_image]
   exact Submodule.mem_map_of_mem h
 #align submodule.apply_mem_span_image_of_mem_span Submodule.apply_mem_span_image_of_mem_span
 
-theorem apply_mem_span_image_iff_mem_span [RingHomSurjective σ₁₂] {f : M →ₛₗ[σ₁₂] M₂} {x : M}
+theorem apply_mem_span_image_iff_mem_span [RingHomSurjective σ₁₂] {f : F} {x : M}
     {s : Set M} (hf : Function.Injective f) :
     f x ∈ Submodule.span R₂ (f '' s) ↔ x ∈ Submodule.span R s := by
   rw [← Submodule.mem_comap, ← Submodule.map_span, Submodule.comap_map_eq_of_injective hf]
@@ -605,7 +605,7 @@ theorem map_subtype_span_singleton {p : Submodule R M} (x : p) :
 #align submodule.map_subtype_span_singleton Submodule.map_subtype_span_singleton
 
 /-- `f` is an explicit argument so we can `apply` this theorem and obtain `h` as a new goal. -/
-theorem not_mem_span_of_apply_not_mem_span_image [RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂) {x : M}
+theorem not_mem_span_of_apply_not_mem_span_image [RingHomSurjective σ₁₂] (f : F) {x : M}
     {s : Set M} (h : f x ∉ Submodule.span R₂ (f '' s)) : x ∉ Submodule.span R s :=
   h.imp (apply_mem_span_image_of_mem_span f)
 #align submodule.not_mem_span_of_apply_not_mem_span_image Submodule.not_mem_span_of_apply_not_mem_span_image
@@ -837,7 +837,7 @@ variable [Ring R] [AddCommGroup M] [Module R M]
 theorem span_neg (s : Set M) : span R (-s) = span R s :=
   calc
     span R (-s) = span R ((-LinearMap.id : M →ₗ[R] M) '' s) := by simp
-    _ = map (-LinearMap.id) (span R s) := ((-LinearMap.id).map_span _).symm
+    _ = map (-LinearMap.id) (span R s) := (map_span (-LinearMap.id) _).symm
     _ = span R s := by simp
 #align submodule.span_neg Submodule.span_neg
 

• depends on: #5966

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

@@ -3,17 +3,14 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Frédéric Dupuis,
   Heather Macbeth
-
-! This file was ported from Lean 3 source module linear_algebra.span
-! leanprover-community/mathlib commit 10878f6bf1dab863445907ab23fbfcefcb5845d0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.Basic
 import Mathlib.Order.CompactlyGenerated
 import Mathlib.Order.OmegaCompletePartialOrder
 import Mathlib.Tactic.Ring
 
+#align_import linear_algebra.span from "leanprover-community/mathlib"@"10878f6bf1dab863445907ab23fbfcefcb5845d0"
+
 /-!
 # The span of a set of vectors, as a submodule
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

@@ -366,7 +366,7 @@ theorem mem_sup : x ∈ p ⊔ p' ↔ ∃ y ∈ p, ∃ z ∈ p', y + z = x :=
     · exact ⟨0, by simp, 0, by simp⟩
     · rintro _ _ ⟨y₁, hy₁, z₁, hz₁, rfl⟩ ⟨y₂, hy₂, z₂, hz₂, rfl⟩
       exact ⟨_, add_mem hy₁ hy₂, _, add_mem hz₁ hz₂, by
-        rw [add_assoc, add_assoc, ← add_assoc y₂,  ← add_assoc z₁, add_comm y₂]⟩
+        rw [add_assoc, add_assoc, ← add_assoc y₂, ← add_assoc z₁, add_comm y₂]⟩
     · rintro a _ ⟨y, hy, z, hz, rfl⟩
       exact ⟨_, smul_mem _ a hy, _, smul_mem _ a hz, by simp [smul_add]⟩, by
     rintro ⟨y, hy, z, hz, rfl⟩

Also prove extensionality on a codisjoint pair of submodules.

@@ -960,33 +960,38 @@ variable [Semiring R] [AddCommMonoid M] [Module R M]
 
 variable [Semiring R₂] [AddCommMonoid M₂] [Module R₂ M₂]
 
-variable {σ₁₂ : R →+* R₂}
+variable {F : Type _} {σ₁₂ : R →+* R₂} [SemilinearMapClass F σ₁₂ M M₂]
 
-/-- If two linear maps are equal on a set `s`, then they are equal on `Submodule.span s`.
-
-See also `LinearMap.eqOn_span'` for a version using `Set.EqOn`. -/
-theorem eqOn_span {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (H : Set.EqOn f g s) ⦃x⦄ (h : x ∈ span R s) :
-    f x = g x := by refine' span_induction h H _ _ _ <;> simp (config := { contextual := true })
-#align linear_map.eq_on_span LinearMap.eqOn_span
+/-- Two linear maps are equal on `Submodule.span s` iff they are equal on `s`. -/
+theorem eqOn_span_iff {s : Set M} {f g : F} : Set.EqOn f g (span R s) ↔ Set.EqOn f g s := by
+  rw [← le_eqLocus, span_le]; rfl
 
 /-- If two linear maps are equal on a set `s`, then they are equal on `Submodule.span s`.
 
 This version uses `Set.EqOn`, and the hidden argument will expand to `h : x ∈ (span R s : Set M)`.
 See `LinearMap.eqOn_span` for a version that takes `h : x ∈ span R s` as an argument. -/
-theorem eqOn_span' {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (H : Set.EqOn f g s) :
+theorem eqOn_span' {s : Set M} {f g : F} (H : Set.EqOn f g s) :
     Set.EqOn f g (span R s : Set M) :=
-  eqOn_span H
+  eqOn_span_iff.2 H
 #align linear_map.eq_on_span' LinearMap.eqOn_span'
 
+/-- If two linear maps are equal on a set `s`, then they are equal on `Submodule.span s`.
+
+See also `LinearMap.eqOn_span'` for a version using `Set.EqOn`. -/
+theorem eqOn_span {s : Set M} {f g : F} (H : Set.EqOn f g s) ⦃x⦄ (h : x ∈ span R s) :
+    f x = g x :=
+  eqOn_span' H h
+#align linear_map.eq_on_span LinearMap.eqOn_span
+
 /-- If `s` generates the whole module and linear maps `f`, `g` are equal on `s`, then they are
 equal. -/
-theorem ext_on {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (hv : span R s = ⊤) (h : Set.EqOn f g s) : f = g :=
-  LinearMap.ext fun _ => eqOn_span h (eq_top_iff'.1 hv _)
+theorem ext_on {s : Set M} {f g : F} (hv : span R s = ⊤) (h : Set.EqOn f g s) : f = g :=
+  FunLike.ext _ _ fun _ => eqOn_span h (eq_top_iff'.1 hv _)
 #align linear_map.ext_on LinearMap.ext_on
 
 /-- If the range of `v : ι → M` generates the whole module and linear maps `f`, `g` are equal at
 each `v i`, then they are equal. -/
-theorem ext_on_range {ι : Type _} {v : ι → M} {f g : M →ₛₗ[σ₁₂] M₂} (hv : span R (Set.range v) = ⊤)
+theorem ext_on_range {ι : Type _} {v : ι → M} {f g : F} (hv : span R (Set.range v) = ⊤)
     (h : ∀ i, f (v i) = g (v i)) : f = g :=
   ext_on hv (Set.forall_range_iff.2 h)
 #align linear_map.ext_on_range LinearMap.ext_on_range

Add the other direction and iff version of submodule.apply_mem_span_image_of_mem_span, that is:

theorem apply_mem_span_image_iff_mem_span [RingHomSurjective σ₁₂] {f : M →ₛₗ[σ₁₂] M₂} {x : M} {s : Set M} 
    (hf : Function.Injective f) :  f x ∈ Submodule.span R₂ (f '' s) ↔ x ∈ Submodule.span R s

@@ -597,6 +597,11 @@ theorem apply_mem_span_image_of_mem_span [RingHomSurjective σ₁₂] (f : M →
   exact Submodule.mem_map_of_mem h
 #align submodule.apply_mem_span_image_of_mem_span Submodule.apply_mem_span_image_of_mem_span
 
+theorem apply_mem_span_image_iff_mem_span [RingHomSurjective σ₁₂] {f : M →ₛₗ[σ₁₂] M₂} {x : M}
+    {s : Set M} (hf : Function.Injective f) :
+    f x ∈ Submodule.span R₂ (f '' s) ↔ x ∈ Submodule.span R s := by
+  rw [← Submodule.mem_comap, ← Submodule.map_span, Submodule.comap_map_eq_of_injective hf]
+
 @[simp]
 theorem map_subtype_span_singleton {p : Submodule R M} (x : p) :
     map p.subtype (R ∙ x) = R ∙ (x : M) := by simp [← span_image]

@@ -296,7 +296,7 @@ theorem subset_span_trans {U V W : Set M} (hUV : U ⊆ Submodule.span R V)
   (Submodule.gi R M).gc.le_u_l_trans hUV hVW
 #align submodule.subset_span_trans Submodule.subset_span_trans
 
-/-- See `submodule.span_smul_eq` (in `ring_theory.ideal.operations`) for
+/-- See `submodule.span_smul_eq` (in `RingTheory.Ideal.Operations`) for
 `span R (r • s) = r • span R s` that holds for arbitrary `r` in a `CommSemiring`. -/
 theorem span_smul_eq_of_isUnit (s : Set M) (r : R) (hr : IsUnit r) : span R (r • s) = span R s := by
   apply le_antisymm

This continues the non-unital-ization of mathlib.

• depends on: #5151

@@ -154,6 +154,20 @@ theorem span_induction {p : M → Prop} (h : x ∈ span R s) (Hs : ∀ x ∈ s,
   ((@span_le (p := ⟨ ⟨⟨p, by intros x y; exact H1 x y⟩, H0⟩, H2⟩)) s).2 Hs h
 #align submodule.span_induction Submodule.span_induction
 
+/-- An induction principle for span membership. This is a version of `Submodule.span_induction`
+for binary predicates. -/
+theorem span_induction₂ {p : M → M → Prop} (ha : a ∈ Submodule.span R s)
+    (hb : b ∈ Submodule.span R s) (Hs : ∀ x ∈ s, ∀ y ∈ s, p x y)
+    (H0_left : ∀ y, p 0 y) (H0_right : ∀ x, p x 0)
+    (Hadd_left : ∀ x₁ x₂ y, p x₁ y → p x₂ y → p (x₁ + x₂) y)
+    (Hadd_right : ∀ x y₁ y₂, p x y₁ → p x y₂ → p x (y₁ + y₂))
+    (Hsmul_left : ∀ (r : R) x y, p x y → p (r • x) y)
+    (Hsmul_right : ∀ (r : R) x y, p x y → p x (r • y)) : p a b :=
+  Submodule.span_induction ha
+    (fun x hx => Submodule.span_induction hb (Hs x hx) (H0_right x) (Hadd_right x) fun r =>
+      Hsmul_right r x)
+    (H0_left b) (fun x₁ x₂ => Hadd_left x₁ x₂ b) fun r x => Hsmul_left r x b
+
 /-- A dependent version of `Submodule.span_induction`. -/
 theorem span_induction' {p : ∀ x, x ∈ span R s → Prop}
     (Hs : ∀ (x) (h : x ∈ s), p x (subset_span h))

@@ -594,12 +594,12 @@ theorem not_mem_span_of_apply_not_mem_span_image [RingHomSurjective σ₁₂] (f
   h.imp (apply_mem_span_image_of_mem_span f)
 #align submodule.not_mem_span_of_apply_not_mem_span_image Submodule.not_mem_span_of_apply_not_mem_span_image
 
-theorem iSup_span {ι : Sort _} (p : ι → Set M) : (⨆ i, span R (p i)) = span R (⋃ i, p i) :=
+theorem iSup_span {ι : Sort _} (p : ι → Set M) : ⨆ i, span R (p i) = span R (⋃ i, p i) :=
   le_antisymm (iSup_le fun i => span_mono <| subset_iUnion _ i) <|
     span_le.mpr <| iUnion_subset fun i _ hm => mem_iSup_of_mem i <| subset_span hm
 #align submodule.supr_span Submodule.iSup_span
 
-theorem iSup_eq_span {ι : Sort _} (p : ι → Submodule R M) : (⨆ i, p i) = span R (⋃ i, ↑(p i)) := by
+theorem iSup_eq_span {ι : Sort _} (p : ι → Submodule R M) : ⨆ i, p i = span R (⋃ i, ↑(p i)) := by
   simp_rw [← iSup_span, span_eq]
 #align submodule.supr_eq_span Submodule.iSup_eq_span
 

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.

@@ -117,7 +117,7 @@ alias Submodule.map_span_le ← _root_.LinearMap.map_span_le
 @[simp]
 theorem span_insert_zero : span R (insert (0 : M) s) = span R s := by
   refine' le_antisymm _ (Submodule.span_mono (Set.subset_insert 0 s))
-  rw [span_le, Set.insert_subset]
+  rw [span_le, Set.insert_subset_iff]
   exact ⟨by simp only [SetLike.mem_coe, Submodule.zero_mem], Submodule.subset_span⟩
 #align submodule.span_insert_zero Submodule.span_insert_zero
 
@@ -492,7 +492,7 @@ theorem span_insert (x) (s : Set M) : span R (insert x s) = span R ({x} : Set M)
 #align submodule.span_insert Submodule.span_insert
 
 theorem span_insert_eq_span (h : x ∈ span R s) : span R (insert x s) = span R s :=
-  span_eq_of_le _ (Set.insert_subset.mpr ⟨h, subset_span⟩) (span_mono <| subset_insert _ _)
+  span_eq_of_le _ (Set.insert_subset_iff.mpr ⟨h, subset_span⟩) (span_mono <| subset_insert _ _)
 #align submodule.span_insert_eq_span Submodule.span_insert_eq_span
 
 theorem span_span : span R (span R s : Set M) = span R s :=

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

@@ -359,7 +359,7 @@ theorem mem_sup : x ∈ p ⊔ p' ↔ ∃ y ∈ p, ∃ z ∈ p', y + z = x :=
     exact add_mem ((le_sup_left : p ≤ p ⊔ p') hy) ((le_sup_right : p' ≤ p ⊔ p') hz)⟩
 #align submodule.mem_sup Submodule.mem_sup
 
-theorem mem_sup' : x ∈ p ⊔ p' ↔ ∃ (y : p)(z : p'), (y : M) + z = x :=
+theorem mem_sup' : x ∈ p ⊔ p' ↔ ∃ (y : p) (z : p'), (y : M) + z = x :=
   mem_sup.trans <| by simp only [Subtype.exists, exists_prop]
 #align submodule.mem_sup' Submodule.mem_sup'
 

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

@@ -5,7 +5,7 @@ Authors: Johannes Hölzl, Mario Carneiro, Kevin Buzzard, Yury Kudryashov, Fréd
   Heather Macbeth
 
 ! This file was ported from Lean 3 source module linear_algebra.span
-! leanprover-community/mathlib commit dc6c365e751e34d100e80fe6e314c3c3e0fd2988
+! leanprover-community/mathlib commit 10878f6bf1dab863445907ab23fbfcefcb5845d0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -974,6 +974,17 @@ theorem ext_on_range {ι : Type _} {v : ι → M} {f g : M →ₛₗ[σ₁₂] M
 
 end AddCommMonoid
 
+section NoZeroDivisors
+
+variable (R M)
+variable [Ring R] [AddCommGroup M] [Module R M] [NoZeroSMulDivisors R M]
+
+theorem ker_toSpanSingleton {x : M} (h : x ≠ 0) : LinearMap.ker (toSpanSingleton R M x) = ⊥ :=
+  SetLike.ext fun _ => smul_eq_zero.trans <| or_iff_left_of_imp fun h' => (h h').elim
+#align linear_map.ker_to_span_singleton LinearMap.ker_toSpanSingleton
+
+end NoZeroDivisors
+
 section Field
 
 variable [Field K] [AddCommGroup V] [Module K V]
@@ -991,26 +1002,6 @@ theorem span_singleton_sup_ker_eq_top (f : V →ₗ[K] K) {x : V} (hx : f x ≠
           by simp only [add_sub_cancel'_right]⟩⟩
 #align linear_map.span_singleton_sup_ker_eq_top LinearMap.span_singleton_sup_ker_eq_top
 
-variable (K V)
-
-theorem ker_toSpanSingleton {x : V} (h : x ≠ 0) : LinearMap.ker (toSpanSingleton K V x) = ⊥ := by
-  ext c; constructor
-  · intro hc
-    rw [Submodule.mem_bot]
-    rw [mem_ker] at hc
-    by_contra hc'
-    have : x = 0
-    calc
-      x = c⁻¹ • c • x := by rw [← mul_smul, inv_mul_cancel hc', one_smul]
-      _ = c⁻¹ • (toSpanSingleton K V x) c := rfl
-      _ = 0 := by rw [hc, smul_zero]
-    tauto
-  · rw [mem_ker, Submodule.mem_bot]
-    intro h
-    rw [h]
-    simp
-#align linear_map.ker_to_span_singleton LinearMap.ker_toSpanSingleton
-
 end Field
 
 end LinearMap
@@ -1019,41 +1010,40 @@ open LinearMap
 
 namespace LinearEquiv
 
-section Field
-
-variable (K V) [Field K] [AddCommGroup V] [Module K V]
+variable (R M)
+variable [Ring R] [AddCommGroup M] [Module R M] [NoZeroSMulDivisors R M] (x : M) (h : x ≠ 0)
 
-/-- Given a nonzero element `x` of a vector space `V` over a field `K`, the natural
-    map from `K` to the span of `x`, with invertibility check to consider it as an
-    isomorphism.-/
+/-- Given a nonzero element `x` of a torsion-free module `M` over a ring `R`, the natural
+isomorphism from `R` to the span of `x` given by $r \mapsto r \cdot x$. -/
 noncomputable
-def toSpanNonzeroSingleton (x : V) (h : x ≠ 0) : K ≃ₗ[K] K ∙ x :=
+def toSpanNonzeroSingleton : R ≃ₗ[R] R ∙ x :=
   LinearEquiv.trans
-    (LinearEquiv.ofInjective (LinearMap.toSpanSingleton K V x)
-      (ker_eq_bot.1 <| LinearMap.ker_toSpanSingleton K V h))
-    (LinearEquiv.ofEq (range $ toSpanSingleton K V x) (K ∙ x) (span_singleton_eq_range K V x).symm)
+    (LinearEquiv.ofInjective (LinearMap.toSpanSingleton R M x)
+      (ker_eq_bot.1 <| ker_toSpanSingleton R M h))
+    (LinearEquiv.ofEq (range $ toSpanSingleton R M x) (R ∙ x) (span_singleton_eq_range R M x).symm)
 #align linear_equiv.to_span_nonzero_singleton LinearEquiv.toSpanNonzeroSingleton
 
-theorem toSpanNonzeroSingleton_one (x : V) (h : x ≠ 0) :
-    LinearEquiv.toSpanNonzeroSingleton K V x h 1 =
-      (⟨x, Submodule.mem_span_singleton_self x⟩ : K ∙ x) := by
+theorem toSpanNonzeroSingleton_one :
+    LinearEquiv.toSpanNonzeroSingleton R M x h 1 =
+      (⟨x, Submodule.mem_span_singleton_self x⟩ : R ∙ x) := by
   apply SetLike.coe_eq_coe.mp
-  have : ↑(toSpanNonzeroSingleton K V x h 1) = toSpanSingleton K V x 1 := rfl
+  have : ↑(toSpanNonzeroSingleton R M x h 1) = toSpanSingleton R M x 1 := rfl
   rw [this, toSpanSingleton_one, Submodule.coe_mk]
 #align linear_equiv.to_span_nonzero_singleton_one LinearEquiv.toSpanNonzeroSingleton_one
 
-/-- Given a nonzero element `x` of a vector space `V` over a field `K`, the natural map
-    from the span of `x` to `K`.-/
+/-- Given a nonzero element `x` of a torsion-free module `M` over a ring `R`, the natural
+isomorphism from the span of `x` to `R` given by $r \cdot x \mapsto r$. -/
 noncomputable
-abbrev coord (x : V) (h : x ≠ 0) : (K ∙ x) ≃ₗ[K] K :=
-  (toSpanNonzeroSingleton K V x h).symm
+abbrev coord : (R ∙ x) ≃ₗ[R] R :=
+  (toSpanNonzeroSingleton R M x h).symm
 #align linear_equiv.coord LinearEquiv.coord
 
-theorem coord_self (x : V) (h : x ≠ 0) :
-    (coord K V x h) (⟨x, Submodule.mem_span_singleton_self x⟩ : K ∙ x) = 1 := by
-  rw [← toSpanNonzeroSingleton_one K V x h, LinearEquiv.symm_apply_apply]
+theorem coord_self : (coord R M x h) (⟨x, Submodule.mem_span_singleton_self x⟩ : R ∙ x) = 1 := by
+  rw [← toSpanNonzeroSingleton_one R M x h, LinearEquiv.symm_apply_apply]
 #align linear_equiv.coord_self LinearEquiv.coord_self
 
-end Field
+theorem coord_apply_smul (y : Submodule.span R ({x} : Set M)) : coord R M x h y • x = y :=
+  Subtype.ext_iff.1 <| (toSpanNonzeroSingleton R M x h).apply_symm_apply _
+#align linear_equiv.coord_apply_smul LinearEquiv.coord_apply_smul
 
 end LinearEquiv

Currently, the following notations are changed from · ×ˢ · because Lean 4 can't deal with ambiguous notations. | Definition | Notation | | :

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com>

@@ -760,18 +760,15 @@ end
 
 variable {M' : Type _} [AddCommMonoid M'] [Module R M'] (q₁ q₁' : Submodule R M')
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The product of two submodules is a submodule. -/
 def prod : Submodule R (M × M') :=
-  {
-    p.toAddSubmonoid.prod q₁.toAddSubmonoid with
+  { p.toAddSubmonoid.prod q₁.toAddSubmonoid with
     carrier := p ×ˢ q₁
     smul_mem' := by rintro a ⟨x, y⟩ ⟨hx, hy⟩; exact ⟨smul_mem _ a hx, smul_mem _ a hy⟩ }
 #align submodule.prod Submodule.prod
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
-theorem prod_coe : (prod p q₁ : Set (M × M')) = p ×ˢ q₁ :=
+theorem prod_coe : (prod p q₁ : Set (M × M')) = (p : Set M) ×ˢ (q₁ : Set M') :=
   rfl
 #align submodule.prod_coe Submodule.prod_coe
 
@@ -781,7 +778,6 @@ theorem mem_prod {p : Submodule R M} {q : Submodule R M'} {x : M × M'} :
   Set.mem_prod
 #align submodule.mem_prod Submodule.mem_prod
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem span_prod_le (s : Set M) (t : Set M') : span R (s ×ˢ t) ≤ prod (span R s) (span R t) :=
   span_le.2 <| Set.prod_mono subset_span subset_span
 #align submodule.span_prod_le Submodule.span_prod_le

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

@@ -17,7 +17,7 @@ import Mathlib.Tactic.Ring
 /-!
 # The span of a set of vectors, as a submodule
 
-* `submodule.span s` is defined to be the smallest submodule containing the set `s`.
+* `Submodule.span s` is defined to be the smallest submodule containing the set `s`.
 
 ## Notations
 
@@ -88,7 +88,7 @@ theorem span_eq_span (hs : s ⊆ span R t) (ht : t ⊆ span R s) : span R s = sp
   le_antisymm (span_le.2 hs) (span_le.2 ht)
 #align submodule.span_eq_span Submodule.span_eq_span
 
-/-- A version of `submodule.span_eq` for when the span is by a smaller ring. -/
+/-- A version of `Submodule.span_eq` for when the span is by a smaller ring. -/
 @[simp]
 theorem span_coe_eq_restrictScalars [Semiring S] [SMul S R] [Module S M] [IsScalarTower S R M] :
     span S (p : Set M) = p.restrictScalars S :=
@@ -283,7 +283,7 @@ theorem subset_span_trans {U V W : Set M} (hUV : U ⊆ Submodule.span R V)
 #align submodule.subset_span_trans Submodule.subset_span_trans
 
 /-- See `submodule.span_smul_eq` (in `ring_theory.ideal.operations`) for
-`span R (r • s) = r • span R s` that holds for arbitrary `r` in a `comm_semiring`. -/
+`span R (r • s) = r • span R s` that holds for arbitrary `r` in a `CommSemiring`. -/
 theorem span_smul_eq_of_isUnit (s : Set M) (r : R) (hr : IsUnit r) : span R (r • s) = span R s := by
   apply le_antisymm
   · apply span_smul_le
@@ -507,7 +507,7 @@ theorem span_le_restrictScalars [Semiring S] [SMul R S] [Module S M] [IsScalarTo
   Submodule.span_le.2 Submodule.subset_span
 #align submodule.span_le_restrict_scalars Submodule.span_le_restrictScalars
 
-/-- A version of `submodule.span_le_restrict_scalars` with coercions. -/
+/-- A version of `Submodule.span_le_restrictScalars` with coercions. -/
 @[simp]
 theorem span_subset_span [Semiring S] [SMul R S] [Module S M] [IsScalarTower R S M] :
     ↑(span R s) ⊆ (span S s : Set M) :=
@@ -947,17 +947,17 @@ variable [Semiring R₂] [AddCommMonoid M₂] [Module R₂ M₂]
 
 variable {σ₁₂ : R →+* R₂}
 
-/-- If two linear maps are equal on a set `s`, then they are equal on `submodule.span s`.
+/-- If two linear maps are equal on a set `s`, then they are equal on `Submodule.span s`.
 
-See also `linear_map.eq_on_span'` for a version using `set.eq_on`. -/
+See also `LinearMap.eqOn_span'` for a version using `Set.EqOn`. -/
 theorem eqOn_span {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (H : Set.EqOn f g s) ⦃x⦄ (h : x ∈ span R s) :
     f x = g x := by refine' span_induction h H _ _ _ <;> simp (config := { contextual := true })
 #align linear_map.eq_on_span LinearMap.eqOn_span
 
-/-- If two linear maps are equal on a set `s`, then they are equal on `submodule.span s`.
+/-- If two linear maps are equal on a set `s`, then they are equal on `Submodule.span s`.
 
-This version uses `set.eq_on`, and the hidden argument will expand to `h : x ∈ (span R s : set M)`.
-See `linear_map.eq_on_span` for a version that takes `h : x ∈ span R s` as an argument. -/
+This version uses `Set.EqOn`, and the hidden argument will expand to `h : x ∈ (span R s : Set M)`.
+See `LinearMap.eqOn_span` for a version that takes `h : x ∈ span R s` as an argument. -/
 theorem eqOn_span' {s : Set M} {f g : M →ₛₗ[σ₁₂] M₂} (H : Set.EqOn f g s) :
     Set.EqOn f g (span R s : Set M) :=
   eqOn_span H

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>

@@ -984,7 +984,6 @@ variable [Field K] [AddCommGroup V] [Module K V]
 
 open Classical
 
-set_option synthInstance.etaExperiment true in
 theorem span_singleton_sup_ker_eq_top (f : V →ₗ[K] K) {x : V} (hx : f x ≠ 0) :
     (K ∙ x) ⊔ ker f = ⊤ :=
   eq_top_iff.2 fun y _ =>
@@ -1028,7 +1027,6 @@ section Field
 
 variable (K V) [Field K] [AddCommGroup V] [Module K V]
 
-set_option synthInstance.etaExperiment true in
 /-- Given a nonzero element `x` of a vector space `V` over a field `K`, the natural
     map from `K` to the span of `x`, with invertibility check to consider it as an
     isomorphism.-/
@@ -1040,7 +1038,6 @@ def toSpanNonzeroSingleton (x : V) (h : x ≠ 0) : K ≃ₗ[K] K ∙ x :=
     (LinearEquiv.ofEq (range $ toSpanSingleton K V x) (K ∙ x) (span_singleton_eq_range K V x).symm)
 #align linear_equiv.to_span_nonzero_singleton LinearEquiv.toSpanNonzeroSingleton
 
-set_option synthInstance.etaExperiment true in
 theorem toSpanNonzeroSingleton_one (x : V) (h : x ≠ 0) :
     LinearEquiv.toSpanNonzeroSingleton K V x h 1 =
       (⟨x, Submodule.mem_span_singleton_self x⟩ : K ∙ x) := by
@@ -1049,7 +1046,6 @@ theorem toSpanNonzeroSingleton_one (x : V) (h : x ≠ 0) :
   rw [this, toSpanSingleton_one, Submodule.coe_mk]
 #align linear_equiv.to_span_nonzero_singleton_one LinearEquiv.toSpanNonzeroSingleton_one
 
-set_option synthInstance.etaExperiment true in
 /-- Given a nonzero element `x` of a vector space `V` over a field `K`, the natural map
     from the span of `x` to `K`.-/
 noncomputable
@@ -1057,7 +1053,6 @@ abbrev coord (x : V) (h : x ≠ 0) : (K ∙ x) ≃ₗ[K] K :=
   (toSpanNonzeroSingleton K V x h).symm
 #align linear_equiv.coord LinearEquiv.coord
 
-set_option synthInstance.etaExperiment true in
 theorem coord_self (x : V) (h : x ≠ 0) :
     (coord K V x h) (⟨x, Submodule.mem_span_singleton_self x⟩ : K ∙ x) = 1 := by
   rw [← toSpanNonzeroSingleton_one K V x h, LinearEquiv.symm_apply_apply]

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>

@@ -51,7 +51,7 @@ variable (R)
 
 /-- The span of a set `s ⊆ M` is the smallest submodule of M that contains `s`. -/
 def span (s : Set M) : Submodule R M :=
-  infₛ { p | s ⊆ p }
+  sInf { p | s ⊆ p }
 #align submodule.span Submodule.span
 
 end
@@ -59,7 +59,7 @@ end
 variable {s t : Set M}
 
 theorem mem_span : x ∈ span R s ↔ ∀ p : Submodule R M, s ⊆ p → x ∈ p :=
-  mem_interᵢ₂
+  mem_iInter₂
 #align submodule.mem_span Submodule.mem_span
 
 theorem subset_span : s ⊆ span R s := fun _ h => mem_span.2 fun _ hp => hp h
@@ -236,20 +236,20 @@ theorem span_union (s t : Set M) : span R (s ∪ t) = span R s ⊔ span R t :=
   (Submodule.gi R M).gc.l_sup
 #align submodule.span_union Submodule.span_union
 
-theorem span_unionᵢ {ι} (s : ι → Set M) : span R (⋃ i, s i) = ⨆ i, span R (s i) :=
-  (Submodule.gi R M).gc.l_supᵢ
-#align submodule.span_Union Submodule.span_unionᵢ
+theorem span_iUnion {ι} (s : ι → Set M) : span R (⋃ i, s i) = ⨆ i, span R (s i) :=
+  (Submodule.gi R M).gc.l_iSup
+#align submodule.span_Union Submodule.span_iUnion
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem span_unionᵢ₂ {ι} {κ : ι → Sort _} (s : ∀ i, κ i → Set M) :
+theorem span_iUnion₂ {ι} {κ : ι → Sort _} (s : ∀ i, κ i → Set M) :
     span R (⋃ (i) (j), s i j) = ⨆ (i) (j), span R (s i j) :=
-  (Submodule.gi R M).gc.l_supᵢ₂
-#align submodule.span_Union₂ Submodule.span_unionᵢ₂
+  (Submodule.gi R M).gc.l_iSup₂
+#align submodule.span_Union₂ Submodule.span_iUnion₂
 
-theorem span_attach_bunionᵢ [DecidableEq M] {α : Type _} (s : Finset α) (f : s → Finset M) :
-    span R (s.attach.bunionᵢ f : Set M) = ⨆ x, span R (f x) := by simp [span_unionᵢ]
-#align submodule.span_attach_bUnion Submodule.span_attach_bunionᵢ
+theorem span_attach_biUnion [DecidableEq M] {α : Type _} (s : Finset α) (f : s → Finset M) :
+    span R (s.attach.biUnion f : Set M) = ⨆ x, span R (f x) := by simp [span_iUnion]
+#align submodule.span_attach_bUnion Submodule.span_attach_biUnion
 
 theorem sup_span : p ⊔ span R s = span R (p ∪ s) := by rw [Submodule.span_union, p.span_eq]
 #align submodule.sup_span Submodule.sup_span
@@ -263,13 +263,13 @@ notation:1000
 character `•` U+2022 and the matrix multiplication character `⬝` U+2B1D. -/
 R " ∙ " x => span R (singleton x)
 
-theorem span_eq_supᵢ_of_singleton_spans (s : Set M) : span R s = ⨆ x ∈ s, R ∙ x := by
-  simp only [← span_unionᵢ, Set.bunionᵢ_of_singleton s]
-#align submodule.span_eq_supr_of_singleton_spans Submodule.span_eq_supᵢ_of_singleton_spans
+theorem span_eq_iSup_of_singleton_spans (s : Set M) : span R s = ⨆ x ∈ s, R ∙ x := by
+  simp only [← span_iUnion, Set.biUnion_of_singleton s]
+#align submodule.span_eq_supr_of_singleton_spans Submodule.span_eq_iSup_of_singleton_spans
 
-theorem span_range_eq_supᵢ {ι : Type _} {v : ι → M} : span R (range v) = ⨆ i, R ∙ v i := by
-  rw [span_eq_supᵢ_of_singleton_spans, supᵢ_range]
-#align submodule.span_range_eq_supr Submodule.span_range_eq_supᵢ
+theorem span_range_eq_iSup {ι : Type _} {v : ι → M} : span R (range v) = ⨆ i, R ∙ v i := by
+  rw [span_eq_iSup_of_singleton_spans, iSup_range]
+#align submodule.span_range_eq_supr Submodule.span_range_eq_iSup
 
 theorem span_smul_le (s : Set M) (r : R) : span R (r • s) ≤ span R s := by
   rw [span_le]
@@ -294,49 +294,49 @@ theorem span_smul_eq_of_isUnit (s : Set M) (r : R) (hr : IsUnit r) : span R (r 
 #align submodule.span_smul_eq_of_is_unit Submodule.span_smul_eq_of_isUnit
 
 @[simp]
-theorem coe_supᵢ_of_directed {ι} [hι : Nonempty ι] (S : ι → Submodule R M)
-    (H : Directed (· ≤ ·) S) : ((supᵢ S : Submodule R M) : Set M) = ⋃ i, S i := by
-  refine' Subset.antisymm _ (unionᵢ_subset <| le_supᵢ S)
+theorem coe_iSup_of_directed {ι} [hι : Nonempty ι] (S : ι → Submodule R M)
+    (H : Directed (· ≤ ·) S) : ((iSup S : Submodule R M) : Set M) = ⋃ i, S i := by
+  refine' Subset.antisymm _ (iUnion_subset <| le_iSup S)
   suffices (span R (⋃ i, (S i : Set M)) : Set M) ⊆ ⋃ i : ι, ↑(S i) by
-    simpa only [span_unionᵢ, span_eq] using this
-  refine' fun x hx => span_induction hx (fun _ => id) _ _ _ <;> simp only [mem_unionᵢ, exists_imp]
+    simpa only [span_iUnion, span_eq] using this
+  refine' fun x hx => span_induction hx (fun _ => id) _ _ _ <;> simp only [mem_iUnion, exists_imp]
   · exact hι.elim fun i => ⟨i, (S i).zero_mem⟩
   · intro x y i hi j hj
     rcases H i j with ⟨k, ik, jk⟩
     exact ⟨k, add_mem (ik hi) (jk hj)⟩
   · exact fun a x i hi => ⟨i, smul_mem _ a hi⟩
-#align submodule.coe_supr_of_directed Submodule.coe_supᵢ_of_directed
+#align submodule.coe_supr_of_directed Submodule.coe_iSup_of_directed
 
 @[simp]
-theorem mem_supᵢ_of_directed {ι} [Nonempty ι] (S : ι → Submodule R M) (H : Directed (· ≤ ·) S) {x} :
-    x ∈ supᵢ S ↔ ∃ i, x ∈ S i := by
-  rw [← SetLike.mem_coe, coe_supᵢ_of_directed S H, mem_unionᵢ]
+theorem mem_iSup_of_directed {ι} [Nonempty ι] (S : ι → Submodule R M) (H : Directed (· ≤ ·) S) {x} :
+    x ∈ iSup S ↔ ∃ i, x ∈ S i := by
+  rw [← SetLike.mem_coe, coe_iSup_of_directed S H, mem_iUnion]
   rfl
-#align submodule.mem_supr_of_directed Submodule.mem_supᵢ_of_directed
+#align submodule.mem_supr_of_directed Submodule.mem_iSup_of_directed
 
-theorem mem_supₛ_of_directed {s : Set (Submodule R M)} {z} (hs : s.Nonempty)
-    (hdir : DirectedOn (· ≤ ·) s) : z ∈ supₛ s ↔ ∃ y ∈ s, z ∈ y := by
+theorem mem_sSup_of_directed {s : Set (Submodule R M)} {z} (hs : s.Nonempty)
+    (hdir : DirectedOn (· ≤ ·) s) : z ∈ sSup s ↔ ∃ y ∈ s, z ∈ y := by
   have : Nonempty s := hs.to_subtype
-  simp only [supₛ_eq_supᵢ', mem_supᵢ_of_directed _ hdir.directed_val, SetCoe.exists, Subtype.coe_mk,
+  simp only [sSup_eq_iSup', mem_iSup_of_directed _ hdir.directed_val, SetCoe.exists, Subtype.coe_mk,
     exists_prop]
-#align submodule.mem_Sup_of_directed Submodule.mem_supₛ_of_directed
+#align submodule.mem_Sup_of_directed Submodule.mem_sSup_of_directed
 
 @[norm_cast, simp]
-theorem coe_supᵢ_of_chain (a : ℕ →o Submodule R M) : (↑(⨆ k, a k) : Set M) = ⋃ k, (a k : Set M) :=
-  coe_supᵢ_of_directed a a.monotone.directed_le
-#align submodule.coe_supr_of_chain Submodule.coe_supᵢ_of_chain
+theorem coe_iSup_of_chain (a : ℕ →o Submodule R M) : (↑(⨆ k, a k) : Set M) = ⋃ k, (a k : Set M) :=
+  coe_iSup_of_directed a a.monotone.directed_le
+#align submodule.coe_supr_of_chain Submodule.coe_iSup_of_chain
 
-/-- We can regard `coe_supᵢ_of_chain` as the statement that `(↑) : (Submodule R M) → Set M` is
+/-- We can regard `coe_iSup_of_chain` as the statement that `(↑) : (Submodule R M) → Set M` is
 Scott continuous for the ω-complete partial order induced by the complete lattice structures. -/
 theorem coe_scott_continuous :
     OmegaCompletePartialOrder.Continuous' ((↑) : Submodule R M → Set M) :=
-  ⟨SetLike.coe_mono, coe_supᵢ_of_chain⟩
+  ⟨SetLike.coe_mono, coe_iSup_of_chain⟩
 #align submodule.coe_scott_continuous Submodule.coe_scott_continuous
 
 @[simp]
-theorem mem_supᵢ_of_chain (a : ℕ →o Submodule R M) (m : M) : (m ∈ ⨆ k, a k) ↔ ∃ k, m ∈ a k :=
-  mem_supᵢ_of_directed a a.monotone.directed_le
-#align submodule.mem_supr_of_chain Submodule.mem_supᵢ_of_chain
+theorem mem_iSup_of_chain (a : ℕ →o Submodule R M) (m : M) : (m ∈ ⨆ k, a k) ↔ ∃ k, m ∈ a k :=
+  mem_iSup_of_directed a a.monotone.directed_le
+#align submodule.mem_supr_of_chain Submodule.mem_iSup_of_chain
 
 section
 
@@ -594,19 +594,19 @@ theorem not_mem_span_of_apply_not_mem_span_image [RingHomSurjective σ₁₂] (f
   h.imp (apply_mem_span_image_of_mem_span f)
 #align submodule.not_mem_span_of_apply_not_mem_span_image Submodule.not_mem_span_of_apply_not_mem_span_image
 
-theorem supᵢ_span {ι : Sort _} (p : ι → Set M) : (⨆ i, span R (p i)) = span R (⋃ i, p i) :=
-  le_antisymm (supᵢ_le fun i => span_mono <| subset_unionᵢ _ i) <|
-    span_le.mpr <| unionᵢ_subset fun i _ hm => mem_supᵢ_of_mem i <| subset_span hm
-#align submodule.supr_span Submodule.supᵢ_span
+theorem iSup_span {ι : Sort _} (p : ι → Set M) : (⨆ i, span R (p i)) = span R (⋃ i, p i) :=
+  le_antisymm (iSup_le fun i => span_mono <| subset_iUnion _ i) <|
+    span_le.mpr <| iUnion_subset fun i _ hm => mem_iSup_of_mem i <| subset_span hm
+#align submodule.supr_span Submodule.iSup_span
 
-theorem supᵢ_eq_span {ι : Sort _} (p : ι → Submodule R M) : (⨆ i, p i) = span R (⋃ i, ↑(p i)) := by
-  simp_rw [← supᵢ_span, span_eq]
-#align submodule.supr_eq_span Submodule.supᵢ_eq_span
+theorem iSup_eq_span {ι : Sort _} (p : ι → Submodule R M) : (⨆ i, p i) = span R (⋃ i, ↑(p i)) := by
+  simp_rw [← iSup_span, span_eq]
+#align submodule.supr_eq_span Submodule.iSup_eq_span
 
-theorem supᵢ_toAddSubmonoid {ι : Sort _} (p : ι → Submodule R M) :
+theorem iSup_toAddSubmonoid {ι : Sort _} (p : ι → Submodule R M) :
     (⨆ i, p i).toAddSubmonoid = ⨆ i, (p i).toAddSubmonoid := by
-  refine' le_antisymm (fun x => _) (supᵢ_le fun i => toAddSubmonoid_mono <| le_supᵢ _ i)
-  simp_rw [supᵢ_eq_span, AddSubmonoid.supᵢ_eq_closure, mem_toAddSubmonoid, coe_toAddSubmonoid]
+  refine' le_antisymm (fun x => _) (iSup_le fun i => toAddSubmonoid_mono <| le_iSup _ i)
+  simp_rw [iSup_eq_span, AddSubmonoid.iSup_eq_closure, mem_toAddSubmonoid, coe_toAddSubmonoid]
   intro hx
   refine' Submodule.span_induction hx (fun x hx => _) _ (fun x y hx hy => _) fun r x hx => _
   · exact AddSubmonoid.subset_closure hx
@@ -614,40 +614,40 @@ theorem supᵢ_toAddSubmonoid {ι : Sort _} (p : ι → Submodule R M) :
   · exact AddSubmonoid.add_mem _ hx hy
   · refine AddSubmonoid.closure_induction hx ?_ ?_ ?_
     · rintro x ⟨_, ⟨i, rfl⟩, hix : x ∈ p i⟩
-      apply AddSubmonoid.subset_closure (Set.mem_unionᵢ.mpr ⟨i, _⟩)
+      apply AddSubmonoid.subset_closure (Set.mem_iUnion.mpr ⟨i, _⟩)
       exact smul_mem _ r hix
     · rw [smul_zero]
       exact AddSubmonoid.zero_mem _
     · intro x y hx hy
       rw [smul_add]
       exact AddSubmonoid.add_mem _ hx hy
-#align submodule.supr_to_add_submonoid Submodule.supᵢ_toAddSubmonoid
+#align submodule.supr_to_add_submonoid Submodule.iSup_toAddSubmonoid
 
 /-- An induction principle for elements of `⨆ i, p i`.
 If `C` holds for `0` and all elements of `p i` for all `i`, and is preserved under addition,
 then it holds for all elements of the supremum of `p`. -/
 @[elab_as_elim]
-theorem supᵢ_induction {ι : Sort _} (p : ι → Submodule R M) {C : M → Prop} {x : M}
+theorem iSup_induction {ι : Sort _} (p : ι → Submodule R M) {C : M → Prop} {x : M}
     (hx : x ∈ ⨆ i, p i) (hp : ∀ (i), ∀ x ∈ p i, C x) (h0 : C 0)
     (hadd : ∀ x y, C x → C y → C (x + y)) : C x := by
-  rw [← mem_toAddSubmonoid, supᵢ_toAddSubmonoid] at hx
-  exact AddSubmonoid.supᵢ_induction (x := x) _ hx hp h0 hadd
-#align submodule.supr_induction Submodule.supᵢ_induction
+  rw [← mem_toAddSubmonoid, iSup_toAddSubmonoid] at hx
+  exact AddSubmonoid.iSup_induction (x := x) _ hx hp h0 hadd
+#align submodule.supr_induction Submodule.iSup_induction
 
-/-- A dependent version of `submodule.supᵢ_induction`. -/
+/-- A dependent version of `submodule.iSup_induction`. -/
 @[elab_as_elim]
-theorem supᵢ_induction' {ι : Sort _} (p : ι → Submodule R M) {C : ∀ x, (x ∈ ⨆ i, p i) → Prop}
-    (hp : ∀ (i) (x) (hx : x ∈ p i), C x (mem_supᵢ_of_mem i hx)) (h0 : C 0 (zero_mem _))
+theorem iSup_induction' {ι : Sort _} (p : ι → Submodule R M) {C : ∀ x, (x ∈ ⨆ i, p i) → Prop}
+    (hp : ∀ (i) (x) (hx : x ∈ p i), C x (mem_iSup_of_mem i hx)) (h0 : C 0 (zero_mem _))
     (hadd : ∀ x y hx hy, C x hx → C y hy → C (x + y) (add_mem ‹_› ‹_›)) {x : M}
     (hx : x ∈ ⨆ i, p i) : C x hx := by
   refine' Exists.elim _ fun (hx : x ∈ ⨆ i, p i) (hc : C x hx) => hc
-  refine' supᵢ_induction p (C := fun x : M ↦ ∃ (hx : x ∈ ⨆ i, p i), C x hx) hx
+  refine' iSup_induction p (C := fun x : M ↦ ∃ (hx : x ∈ ⨆ i, p i), C x hx) hx
     (fun i x hx => _) _ fun x y => _
   · exact ⟨_, hp _ _ hx⟩
   · exact ⟨_, h0⟩
   · rintro ⟨_, Cx⟩ ⟨_, Cy⟩
     refine' ⟨_, hadd _ _ _ _ Cx Cy⟩
-#align submodule.supr_induction' Submodule.supᵢ_induction'
+#align submodule.supr_induction' Submodule.iSup_induction'
 
 @[simp]
 theorem span_singleton_le_iff_mem (m : M) (p : Submodule R M) : (R ∙ m) ≤ p ↔ m ∈ p := by
@@ -656,19 +656,19 @@ theorem span_singleton_le_iff_mem (m : M) (p : Submodule R M) : (R ∙ m) ≤ p
 
 theorem singleton_span_isCompactElement (x : M) :
     CompleteLattice.IsCompactElement (span R {x} : Submodule R M) := by
-  rw [CompleteLattice.isCompactElement_iff_le_of_directed_supₛ_le]
+  rw [CompleteLattice.isCompactElement_iff_le_of_directed_sSup_le]
   intro d hemp hdir hsup
-  have : x ∈ (supₛ d) := (SetLike.le_def.mp hsup) (mem_span_singleton_self x)
-  obtain ⟨y, ⟨hyd, hxy⟩⟩ := (mem_supₛ_of_directed hemp hdir).mp this
+  have : x ∈ (sSup d) := (SetLike.le_def.mp hsup) (mem_span_singleton_self x)
+  obtain ⟨y, ⟨hyd, hxy⟩⟩ := (mem_sSup_of_directed hemp hdir).mp this
   exact ⟨y, ⟨hyd, by simpa only [span_le, singleton_subset_iff] ⟩⟩
 #align submodule.singleton_span_is_compact_element Submodule.singleton_span_isCompactElement
 
 /-- The span of a finite subset is compact in the lattice of submodules. -/
 theorem finset_span_isCompactElement (S : Finset M) :
     CompleteLattice.IsCompactElement (span R S : Submodule R M) := by
-  rw [span_eq_supᵢ_of_singleton_spans]
+  rw [span_eq_iSup_of_singleton_spans]
   simp only [Finset.mem_coe]
-  rw [← Finset.sup_eq_supᵢ]
+  rw [← Finset.sup_eq_iSup]
   exact
     CompleteLattice.finset_sup_compact_of_compact S fun x _ => singleton_span_isCompactElement x
 #align submodule.finset_span_is_compact_element Submodule.finset_span_isCompactElement
@@ -685,22 +685,22 @@ instance : IsCompactlyGenerated (Submodule R M) :=
       ⟨fun t ht => by
         rcases(Set.mem_image _ _ _).1 ht with ⟨x, _, rfl⟩
         apply singleton_span_isCompactElement, by
-        rw [supₛ_eq_supᵢ, supᵢ_image, ← span_eq_supᵢ_of_singleton_spans, span_eq]⟩⟩⟩
+        rw [sSup_eq_iSup, iSup_image, ← span_eq_iSup_of_singleton_spans, span_eq]⟩⟩⟩
 
 /-- A submodule is equal to the supremum of the spans of the submodule's nonzero elements. -/
-theorem submodule_eq_supₛ_le_nonzero_spans (p : Submodule R M) :
-    p = supₛ { T : Submodule R M | ∃ (m : M) (_ : m ∈ p) (_ : m ≠ 0), T = span R {m} } := by
+theorem submodule_eq_sSup_le_nonzero_spans (p : Submodule R M) :
+    p = sSup { T : Submodule R M | ∃ (m : M) (_ : m ∈ p) (_ : m ≠ 0), T = span R {m} } := by
   let S := { T : Submodule R M | ∃ (m : M) (_ : m ∈ p) (_ : m ≠ 0), T = span R {m} }
   apply le_antisymm
   · intro m hm
     by_cases h : m = 0
     · rw [h]
       simp
-    · exact @le_supₛ _ _ S _ ⟨m, ⟨hm, ⟨h, rfl⟩⟩⟩ m (mem_span_singleton_self m)
-  · rw [supₛ_le_iff]
+    · exact @le_sSup _ _ S _ ⟨m, ⟨hm, ⟨h, rfl⟩⟩⟩ m (mem_span_singleton_self m)
+  · rw [sSup_le_iff]
     rintro S ⟨_, ⟨_, ⟨_, rfl⟩⟩⟩
     rwa [span_singleton_le_iff_mem]
-#align submodule.submodule_eq_Sup_le_nonzero_spans Submodule.submodule_eq_supₛ_le_nonzero_spans
+#align submodule.submodule_eq_Sup_le_nonzero_spans Submodule.submodule_eq_sSup_le_nonzero_spans
 
 theorem lt_sup_iff_not_mem {I : Submodule R M} {a : M} : (I < I ⊔ R ∙ a) ↔ a ∉ I := by
   constructor
@@ -725,11 +725,11 @@ theorem lt_sup_iff_not_mem {I : Submodule R M} {a : M} : (I < I ⊔ R ∙ a) ↔
       exact this (mem_span_singleton_self a)
 #align submodule.lt_sup_iff_not_mem Submodule.lt_sup_iff_not_mem
 
-theorem mem_supᵢ {ι : Sort _} (p : ι → Submodule R M) {m : M} :
+theorem mem_iSup {ι : Sort _} (p : ι → Submodule R M) {m : M} :
     (m ∈ ⨆ i, p i) ↔ ∀ N, (∀ i, p i ≤ N) → m ∈ N := by
-  rw [← span_singleton_le_iff_mem, le_supᵢ_iff]
+  rw [← span_singleton_le_iff_mem, le_iSup_iff]
   simp only [span_singleton_le_iff_mem]
-#align submodule.mem_supr Submodule.mem_supᵢ
+#align submodule.mem_supr Submodule.mem_iSup
 
 section
 

closes #3680, see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Stepping.20through.20simp_rw/near/326712986

@@ -484,7 +484,7 @@ theorem mem_span_insert {y} :
 
 theorem mem_span_pair {x y z : M} :
     z ∈ span R ({x, y} : Set M) ↔ ∃ a b : R, a • x + b • y = z := by
-  simp_rw [mem_span_insert, mem_span_singleton, exists_prop, exists_exists_eq_and, eq_comm]
+  simp_rw [mem_span_insert, mem_span_singleton, exists_exists_eq_and, eq_comm]
 #align submodule.mem_span_pair Submodule.mem_span_pair
 
 theorem span_insert (x) (s : Set M) : span R (insert x s) = span R ({x} : Set M) ⊔ span R s := by

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>

@@ -984,12 +984,7 @@ variable [Field K] [AddCommGroup V] [Module K V]
 
 open Classical
 
--- 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 K K := Semiring.toModule
-
+set_option synthInstance.etaExperiment true in
 theorem span_singleton_sup_ker_eq_top (f : V →ₗ[K] K) {x : V} (hx : f x ≠ 0) :
     (K ∙ x) ⊔ ker f = ⊤ :=
   eq_top_iff.2 fun y _ =>
@@ -1033,9 +1028,7 @@ section Field
 
 variable (K V) [Field K] [AddCommGroup V] [Module K V]
 
--- Porting note: TODO Erase this line. Needed because we don't have η for classes. (lean4#2074)
-attribute [-instance] Ring.toNonAssocRing
-
+set_option synthInstance.etaExperiment true in
 /-- Given a nonzero element `x` of a vector space `V` over a field `K`, the natural
     map from `K` to the span of `x`, with invertibility check to consider it as an
     isomorphism.-/
@@ -1047,6 +1040,7 @@ def toSpanNonzeroSingleton (x : V) (h : x ≠ 0) : K ≃ₗ[K] K ∙ x :=
     (LinearEquiv.ofEq (range $ toSpanSingleton K V x) (K ∙ x) (span_singleton_eq_range K V x).symm)
 #align linear_equiv.to_span_nonzero_singleton LinearEquiv.toSpanNonzeroSingleton
 
+set_option synthInstance.etaExperiment true in
 theorem toSpanNonzeroSingleton_one (x : V) (h : x ≠ 0) :
     LinearEquiv.toSpanNonzeroSingleton K V x h 1 =
       (⟨x, Submodule.mem_span_singleton_self x⟩ : K ∙ x) := by
@@ -1055,6 +1049,7 @@ theorem toSpanNonzeroSingleton_one (x : V) (h : x ≠ 0) :
   rw [this, toSpanSingleton_one, Submodule.coe_mk]
 #align linear_equiv.to_span_nonzero_singleton_one LinearEquiv.toSpanNonzeroSingleton_one
 
+set_option synthInstance.etaExperiment true in
 /-- Given a nonzero element `x` of a vector space `V` over a field `K`, the natural map
     from the span of `x` to `K`.-/
 noncomputable
@@ -1062,6 +1057,7 @@ abbrev coord (x : V) (h : x ≠ 0) : (K ∙ x) ≃ₗ[K] K :=
   (toSpanNonzeroSingleton K V x h).symm
 #align linear_equiv.coord LinearEquiv.coord
 
+set_option synthInstance.etaExperiment true in
 theorem coord_self (x : V) (h : x ≠ 0) :
     (coord K V x h) (⟨x, Submodule.mem_span_singleton_self x⟩ : K ∙ x) = 1 := by
   rw [← toSpanNonzeroSingleton_one K V x h, LinearEquiv.symm_apply_apply]

This PR fixes two things:

• Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
• All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

@@ -827,7 +827,6 @@ theorem span_neg (s : Set M) : span R (-s) = span R s :=
     span R (-s) = span R ((-LinearMap.id : M →ₗ[R] M) '' s) := by simp
     _ = map (-LinearMap.id) (span R s) := ((-LinearMap.id).map_span _).symm
     _ = span R s := by simp
-
 #align submodule.span_neg Submodule.span_neg
 
 theorem mem_span_insert' {x y} {s : Set M} :

@@ -612,7 +612,7 @@ theorem supᵢ_toAddSubmonoid {ι : Sort _} (p : ι → Submodule R M) :
   · exact AddSubmonoid.subset_closure hx
   · exact AddSubmonoid.zero_mem _
   · exact AddSubmonoid.add_mem _ hx hy
-  · apply AddSubmonoid.closure_induction hx
+  · refine AddSubmonoid.closure_induction hx ?_ ?_ ?_
     · rintro x ⟨_, ⟨i, rfl⟩, hix : x ∈ p i⟩
       apply AddSubmonoid.subset_closure (Set.mem_unionᵢ.mpr ⟨i, _⟩)
       exact smul_mem _ r hix
@@ -631,7 +631,7 @@ theorem supᵢ_induction {ι : Sort _} (p : ι → Submodule R M) {C : M → Pro
     (hx : x ∈ ⨆ i, p i) (hp : ∀ (i), ∀ x ∈ p i, C x) (h0 : C 0)
     (hadd : ∀ x y, C x → C y → C (x + y)) : C x := by
   rw [← mem_toAddSubmonoid, supᵢ_toAddSubmonoid] at hx
-  exact AddSubmonoid.supᵢ_induction _ hx hp h0 hadd
+  exact AddSubmonoid.supᵢ_induction (x := x) _ hx hp h0 hadd
 #align submodule.supr_induction Submodule.supᵢ_induction
 
 /-- A dependent version of `submodule.supᵢ_induction`. -/

Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: qawbecrdtey <qawbecrdtey@naver.com>