linear_algebra.dimension ⟷ Mathlib.LinearAlgebra.Dimension.StrongRankCondition

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 -/
 import Algebra.Module.BigOperators
-import LinearAlgebra.Dfinsupp
+import LinearAlgebra.DFinsupp
 import LinearAlgebra.FreeModule.Basic
 import LinearAlgebra.InvariantBasisNumber
 import LinearAlgebra.Isomorphisms

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

@@ -188,7 +188,7 @@ theorem lift_rank_map_le (f : M →ₗ[R] M') (p : Submodule R M) :
     Cardinal.lift.{v} (Module.rank R (p.map f)) ≤ Cardinal.lift.{v'} (Module.rank R p) :=
   by
   have h := lift_rank_range_le (f.comp (Submodule.subtype p))
-  rwa [LinearMap.range_comp, range_subtype] at h 
+  rwa [LinearMap.range_comp, range_subtype] at h
 #align lift_rank_map_le lift_rank_map_le
 -/
 
@@ -354,7 +354,7 @@ variable {R M}
 #print exists_mem_ne_zero_of_rank_pos /-
 theorem exists_mem_ne_zero_of_rank_pos {s : Submodule R M} (h : 0 < Module.rank R s) :
     ∃ b : M, b ∈ s ∧ b ≠ 0 :=
-  exists_mem_ne_zero_of_ne_bot fun eq => by rw [Eq, rank_bot] at h  <;> exact lt_irrefl _ h
+  exists_mem_ne_zero_of_ne_bot fun eq => by rw [Eq, rank_bot] at h <;> exact lt_irrefl _ h
 #align exists_mem_ne_zero_of_rank_pos exists_mem_ne_zero_of_rank_pos
 -/
 
@@ -370,7 +370,7 @@ theorem LinearIndependent.finite_of_isNoetherian [IsNoetherian R M] {v : ι →
       fun i contra => _
   apply hv.ne_zero i
   have : v i ∈ R ∙ v i := Submodule.mem_span_singleton_self (v i)
-  rwa [contra, Submodule.mem_bot] at this 
+  rwa [contra, Submodule.mem_bot] at this
 #align linear_independent.finite_of_is_noetherian LinearIndependent.finite_of_isNoetherian
 -/
 
@@ -430,7 +430,7 @@ theorem union_support_maximal_linearIndependent_eq_range_basis {ι : Type w} (b
   -- If that's not the case,
   by_contra h
   simp only [← Ne.def, ne_univ_iff_exists_not_mem, mem_Union, Classical.not_exists_not,
-    Finsupp.mem_support_iff, Finset.mem_coe] at h 
+    Finsupp.mem_support_iff, Finset.mem_coe] at h
   -- We have some basis element `b b'` which is not in the support of any of the `v i`.
   obtain ⟨b', w⟩ := h
   -- Using this, we'll construct a linearly independent family strictly larger than `v`,
@@ -446,7 +446,7 @@ theorem union_support_maximal_linearIndependent_eq_range_basis {ι : Type w} (b
   have r'' : range v ≠ range v' := by
     intro e
     have p : b b' ∈ range v' := by use none; rfl
-    rw [← e] at p 
+    rw [← e] at p
     exact r' p
   have inj' : injective v' := by
     rintro (_ | k) (_ | k) z
@@ -459,30 +459,30 @@ theorem union_support_maximal_linearIndependent_eq_range_basis {ι : Type w} (b
     by
     rw [linearIndependent_subtype_range inj', linearIndependent_iff]
     intro l z
-    rw [Finsupp.total_option] at z 
-    simp only [v', Option.elim'] at z 
-    change _ + Finsupp.total κ M R v l.some = 0 at z 
+    rw [Finsupp.total_option] at z
+    simp only [v', Option.elim'] at z
+    change _ + Finsupp.total κ M R v l.some = 0 at z
     -- We have some linear combination of `b b'` and the `v i`, which we want to show is trivial.
     -- We'll first show the coefficient of `b b'` is zero,
     -- by expressing the `v i` in the basis `b`, and using that the `v i` have no `b b'` term.
     have l₀ : l none = 0 := by
-      rw [← eq_neg_iff_add_eq_zero] at z 
+      rw [← eq_neg_iff_add_eq_zero] at z
       replace z := neg_eq_iff_eq_neg.mpr z
-      apply_fun fun x => b.repr x b' at z 
+      apply_fun fun x => b.repr x b' at z
       simp only [repr_self, LinearEquiv.map_smul, mul_one, Finsupp.single_eq_same, Pi.neg_apply,
-        Finsupp.smul_single', LinearEquiv.map_neg, Finsupp.coe_neg] at z 
-      erw [Finsupp.congr_fun (Finsupp.apply_total R (b.repr : M →ₗ[R] ι →₀ R) v l.some) b'] at z 
+        Finsupp.smul_single', LinearEquiv.map_neg, Finsupp.coe_neg] at z
+      erw [Finsupp.congr_fun (Finsupp.apply_total R (b.repr : M →ₗ[R] ι →₀ R) v l.some) b'] at z
       simpa [Finsupp.total_apply, w] using z
     -- Then all the other coefficients are zero, because `v` is linear independent.
     have l₁ : l.some = 0 := by
-      rw [l₀, zero_smul, zero_add] at z 
+      rw [l₀, zero_smul, zero_add] at z
       exact linear_independent_iff.mp i _ z
     -- Finally we put those facts together to show the linear combination is trivial.
     ext (_ | a)
     · simp only [l₀, Finsupp.coe_zero, Pi.zero_apply]
     · erw [Finsupp.congr_fun l₁ a]
       simp only [Finsupp.coe_zero, Pi.zero_apply]
-  dsimp [LinearIndependent.Maximal] at m 
+  dsimp [LinearIndependent.Maximal] at m
   specialize m (range v') i' r
   exact r'' m
 #align union_support_maximal_linear_independent_eq_range_basis union_support_maximal_linearIndependent_eq_range_basis
@@ -734,9 +734,9 @@ theorem Basis.le_span {J : Set M} (v : Basis ι R M) (hJ : span R J = ⊤) : (#r
       rcases mem_range.1 hb with ⟨i, hi⟩
       have : span R J ≤ comap v.repr.to_linear_map (Finsupp.supported R R (⋃ j, S j)) :=
         span_le.2 fun j hj x hx => ⟨_, ⟨⟨j, hj⟩, rfl⟩, hx⟩
-      rw [hJ] at this 
+      rw [hJ] at this
       replace : v.repr (v i) ∈ Finsupp.supported R R (⋃ j, S j) := this trivial
-      rw [v.repr_self, Finsupp.mem_supported, Finsupp.support_single_ne_zero _ one_ne_zero] at this 
+      rw [v.repr_self, Finsupp.mem_supported, Finsupp.support_single_ne_zero _ one_ne_zero] at this
       · subst b
         rcases mem_Union.1 (this (Finset.mem_singleton_self _)) with ⟨j, hj⟩
         exact mem_Union.2 ⟨j, (mem_image _ _ _).2 ⟨i, hj, rfl⟩⟩
@@ -776,9 +776,9 @@ theorem linearIndependent_le_span_aux' {ι : Type _} [Fintype ι] (v : ι → M)
   · apply Finsupp.total
     exact fun i => Span.repr R w ⟨v i, s (mem_range_self i)⟩
   · intro f g h
-    apply_fun Finsupp.total w M R coe at h 
-    simp only [Finsupp.total_total, Submodule.coe_mk, Span.finsupp_total_repr] at h 
-    rw [← sub_eq_zero, ← LinearMap.map_sub] at h 
+    apply_fun Finsupp.total w M R coe at h
+    simp only [Finsupp.total_total, Submodule.coe_mk, Span.finsupp_total_repr] at h
+    rw [← sub_eq_zero, ← LinearMap.map_sub] at h
     exact sub_eq_zero.mp (linear_independent_iff.mp i _ h)
 #align linear_independent_le_span_aux' linearIndependent_le_span_aux'
 -/
@@ -847,7 +847,7 @@ theorem linearIndependent_le_infinite_basis {ι : Type _} (b : Basis ι R M) [In
     (v : κ → M) (i : LinearIndependent R v) : (#κ) ≤ (#ι) :=
   by
   by_contra
-  rw [not_le, ← Cardinal.mk_finset_of_infinite ι] at h 
+  rw [not_le, ← Cardinal.mk_finset_of_infinite ι] at h
   let Φ := fun k : κ => (b.repr (v k)).support
   obtain ⟨s, w : Infinite ↥(Φ ⁻¹' {s})⟩ := Cardinal.exists_infinite_fiber Φ h (by infer_instance)
   let v' := fun k : Φ ⁻¹' {s} => v k
@@ -991,7 +991,7 @@ theorem Basis.mk_eq_rank'.{m} (v : Basis ι R M) :
 theorem Basis.nonempty_fintype_index_of_rank_lt_aleph0 {ι : Type _} (b : Basis ι R M)
     (h : Module.rank R M < ℵ₀) : Nonempty (Fintype ι) := by
   rwa [← Cardinal.lift_lt, ← b.mk_eq_rank, Cardinal.lift_aleph0, Cardinal.lift_lt_aleph0,
-    Cardinal.lt_aleph0_iff_fintype] at h 
+    Cardinal.lt_aleph0_iff_fintype] at h
 #align basis.nonempty_fintype_index_of_rank_lt_aleph_0 Basis.nonempty_fintype_index_of_rank_lt_aleph0
 -/
 
@@ -1057,7 +1057,7 @@ theorem Ideal.rank_eq {R S : Type _} [CommRing R] [StrongRankCondition R] [Ring
     rw [Fintype.linearIndependent_iff] at hb ⊢
     intro g hg
     apply hb g
-    simp only [← smul_assoc, ← Finset.sum_smul, smul_eq_zero] at hg 
+    simp only [← smul_assoc, ← Finset.sum_smul, smul_eq_zero] at hg
     exact hg.resolve_right ha
   exact
     le_antisymm
@@ -1244,8 +1244,8 @@ def finDimVectorspaceEquiv (n : ℕ) (hn : Module.rank K V = n) : V ≃ₗ[K] Fi
   haveI := nontrivial_of_invariantBasisNumber K
   have : Cardinal.lift.{u} (n : Cardinal.{v}) = Cardinal.lift.{v} (n : Cardinal.{u}) := by simp
   have hn := Cardinal.lift_inj.{v, u}.2 hn
-  rw [this] at hn 
-  rw [← @rank_fin_fun K _ _ n] at hn 
+  rw [this] at hn
+  rw [← @rank_fin_fun K _ _ n] at hn
   haveI : Module.Free K (Fin n → K) := Module.Free.pi _ _
   exact Classical.choice (nonempty_linearEquiv_of_lift_rank_eq hn)
 #align fin_dim_vectorspace_equiv finDimVectorspaceEquiv
@@ -1423,7 +1423,7 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} :
   constructor
   · intro h
     let t := Basis.ofVectorSpace K V
-    rw [← t.mk_eq_rank'', Cardinal.le_mk_iff_exists_subset] at h 
+    rw [← t.mk_eq_rank'', Cardinal.le_mk_iff_exists_subset] at h
     rcases h with ⟨s, hst, hsc⟩
     exact ⟨s, hsc, (of_vector_space_index.linear_independent K V).mono hst⟩
   · rintro ⟨s, rfl, si⟩
@@ -1453,7 +1453,7 @@ theorem rank_le_one_iff : Module.rank K V ≤ 1 ↔ ∃ v₀ : V, ∀ v, ∃ r :
   let b := Basis.ofVectorSpace K V
   constructor
   · intro hd
-    rw [← b.mk_eq_rank'', Cardinal.le_one_iff_subsingleton, subsingleton_coe] at hd 
+    rw [← b.mk_eq_rank'', Cardinal.le_one_iff_subsingleton, subsingleton_coe] at hd
     rcases eq_empty_or_nonempty (of_vector_space_index K V) with (hb | ⟨⟨v₀, hv₀⟩⟩)
     · use 0
       have h' : ∀ v : V, v = 0 := by simpa [hb, Submodule.eq_bot_iff] using b.span_eq.symm
@@ -1463,7 +1463,7 @@ theorem rank_le_one_iff : Module.rank K V ≤ 1 ↔ ∃ v₀ : V, ∀ v, ∃ r :
       have h' : (K ∙ v₀) = ⊤ := by simpa [hd.eq_singleton_of_mem hv₀] using b.span_eq
       intro v
       have hv : v ∈ (⊤ : Submodule K V) := mem_top
-      rwa [← h', mem_span_singleton] at hv 
+      rwa [← h', mem_span_singleton] at hv
   · rintro ⟨v₀, hv₀⟩
     have h : (K ∙ v₀) = ⊤ := by ext; simp [mem_span_singleton, hv₀]
     rw [← rank_top, ← h]
@@ -1486,7 +1486,7 @@ theorem rank_submodule_le_one_iff (s : Submodule K V) :
     intro v hv
     obtain ⟨r, hr⟩ := h ⟨v, hv⟩
     use r
-    simp_rw [Subtype.ext_iff, coe_smul, Submodule.coe_mk] at hr 
+    simp_rw [Subtype.ext_iff, coe_smul, Submodule.coe_mk] at hr
     exact hr
   · rintro ⟨v₀, hv₀, h⟩
     use⟨v₀, hv₀⟩
@@ -1517,8 +1517,8 @@ theorem rank_submodule_le_one_iff' (s : Submodule K V) : Module.rank K s ≤ 1 
         rintro rfl
         simpa using hw0
       rwa [span_singleton_smul_eq (IsUnit.mk0 _ h0) _]
-    · push_neg at hw 
-      rw [← Submodule.eq_bot_iff] at hw 
+    · push_neg at hw
+      rw [← Submodule.eq_bot_iff] at hw
       simp [hw]
 #align rank_submodule_le_one_iff' rank_submodule_le_one_iff'
 -/

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

@@ -1296,7 +1296,10 @@ theorem rank_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V
 
 #print rank_quotient_add_rank /-
 theorem rank_quotient_add_rank (p : Submodule K V) :
-    Module.rank K (V ⧸ p) + Module.rank K p = Module.rank K V := by classical
+    Module.rank K (V ⧸ p) + Module.rank K p = Module.rank K V := by
+  classical exact
+    let ⟨f⟩ := quotient_prod_linearEquiv p
+    rank_prod'.symm.trans f.rank_eq
 #align rank_quotient_add_rank rank_quotient_add_rank
 -/
 

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

@@ -1296,10 +1296,7 @@ theorem rank_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V
 
 #print rank_quotient_add_rank /-
 theorem rank_quotient_add_rank (p : Submodule K V) :
-    Module.rank K (V ⧸ p) + Module.rank K p = Module.rank K V := by
-  classical exact
-    let ⟨f⟩ := quotient_prod_linearEquiv p
-    rank_prod'.symm.trans f.rank_eq
+    Module.rank K (V ⧸ p) + Module.rank K p = Module.rank K V := by classical
 #align rank_quotient_add_rank rank_quotient_add_rank
 -/
 

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

@@ -284,8 +284,8 @@ theorem rank_quotient_le (p : Submodule R M) : Module.rank R (M ⧸ p) ≤ Modul
 
 variable [Nontrivial R]
 
-#print cardinal_lift_le_rank_of_linearIndependent /-
-theorem cardinal_lift_le_rank_of_linearIndependent.{m} {ι : Type w} {v : ι → M}
+#print LinearIndependent.cardinal_lift_le_rank /-
+theorem LinearIndependent.cardinal_lift_le_rank.{m} {ι : Type w} {v : ι → M}
     (hv : LinearIndependent R v) :
     Cardinal.lift.{max v m} (#ι) ≤ Cardinal.lift.{max w m} (Module.rank R M) :=
   by
@@ -296,28 +296,29 @@ theorem cardinal_lift_le_rank_of_linearIndependent.{m} {ι : Type w} {v : ι →
     swap
     exact le_ciSup (Cardinal.bddAbove_range.{v, v} _) ⟨range v, hv.coe_range⟩
     exact le_rfl
-#align cardinal_lift_le_rank_of_linear_independent cardinal_lift_le_rank_of_linearIndependent
+#align cardinal_lift_le_rank_of_linear_independent LinearIndependent.cardinal_lift_le_rank
 -/
 
-#print cardinal_lift_le_rank_of_linearIndependent' /-
-theorem cardinal_lift_le_rank_of_linearIndependent' {ι : Type w} {v : ι → M}
+/- warning: cardinal_lift_le_rank_of_linear_independent' clashes with cardinal_lift_le_rank_of_linear_independent -> LinearIndependent.cardinal_lift_le_rank
+Case conversion may be inaccurate. Consider using '#align cardinal_lift_le_rank_of_linear_independent' LinearIndependent.cardinal_lift_le_rankₓ'. -/
+#print LinearIndependent.cardinal_lift_le_rank /-
+theorem LinearIndependent.cardinal_lift_le_rank {ι : Type w} {v : ι → M}
     (hv : LinearIndependent R v) : Cardinal.lift.{v} (#ι) ≤ Cardinal.lift.{w} (Module.rank R M) :=
-  cardinal_lift_le_rank_of_linearIndependent.{u, v, w, 0} hv
-#align cardinal_lift_le_rank_of_linear_independent' cardinal_lift_le_rank_of_linearIndependent'
+  LinearIndependent.cardinal_lift_le_rank.{u, v, w, 0} hv
+#align cardinal_lift_le_rank_of_linear_independent' LinearIndependent.cardinal_lift_le_rank
 -/
 
-#print cardinal_le_rank_of_linearIndependent /-
-theorem cardinal_le_rank_of_linearIndependent {ι : Type v} {v : ι → M}
-    (hv : LinearIndependent R v) : (#ι) ≤ Module.rank R M := by
-  simpa using cardinal_lift_le_rank_of_linearIndependent hv
-#align cardinal_le_rank_of_linear_independent cardinal_le_rank_of_linearIndependent
+#print LinearIndependent.cardinal_le_rank /-
+theorem LinearIndependent.cardinal_le_rank {ι : Type v} {v : ι → M} (hv : LinearIndependent R v) :
+    (#ι) ≤ Module.rank R M := by simpa using LinearIndependent.cardinal_lift_le_rank hv
+#align cardinal_le_rank_of_linear_independent LinearIndependent.cardinal_le_rank
 -/
 
-#print cardinal_le_rank_of_linearIndependent' /-
-theorem cardinal_le_rank_of_linearIndependent' {s : Set M}
+#print LinearIndependent.cardinal_le_rank' /-
+theorem LinearIndependent.cardinal_le_rank' {s : Set M}
     (hs : LinearIndependent R (fun x => x : s → M)) : (#s) ≤ Module.rank R M :=
-  cardinal_le_rank_of_linearIndependent hs
-#align cardinal_le_rank_of_linear_independent' cardinal_le_rank_of_linearIndependent'
+  LinearIndependent.cardinal_le_rank hs
+#align cardinal_le_rank_of_linear_independent' LinearIndependent.cardinal_le_rank'
 -/
 
 variable (R M)
@@ -531,7 +532,7 @@ theorem CompleteLattice.Independent.subtype_ne_bot_le_rank [NoZeroSMulDivisors R
     exact i.prop
   choose v hvV hv using hI
   have : LinearIndependent R v := (hV.comp Subtype.coe_injective).LinearIndependent _ hvV hv
-  exact cardinal_lift_le_rank_of_linearIndependent' this
+  exact LinearIndependent.cardinal_lift_le_rank this
 #align complete_lattice.independent.subtype_ne_bot_le_rank CompleteLattice.Independent.subtype_ne_bot_le_rank
 -/
 
@@ -572,7 +573,7 @@ theorem rank_pos [Nontrivial M] : 0 < Module.rank R M :=
   suffices 1 ≤ Module.rank R M by exact zero_lt_one.trans_le this
   letI := Module.nontrivial R M
   suffices LinearIndependent R fun y : ({x} : Set M) => ↑y by
-    simpa using cardinal_le_rank_of_linearIndependent this
+    simpa using LinearIndependent.cardinal_le_rank this
   exact linearIndependent_singleton hx
 #align rank_pos rank_pos
 -/
@@ -950,8 +951,7 @@ theorem Basis.card_le_card_of_linearIndependent {ι : Type _} [Fintype ι] (b :
     Fintype.card ι' ≤ Fintype.card ι :=
   by
   letI := nontrivial_of_invariantBasisNumber R
-  simpa [rank_eq_card_basis b, Cardinal.mk_fintype] using
-    cardinal_lift_le_rank_of_linearIndependent' hv
+  simpa [rank_eq_card_basis b, Cardinal.mk_fintype] using LinearIndependent.cardinal_lift_le_rank hv
 #align basis.card_le_card_of_linear_independent Basis.card_le_card_of_linearIndependent
 -/
 
@@ -1427,7 +1427,7 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} :
     rcases h with ⟨s, hst, hsc⟩
     exact ⟨s, hsc, (of_vector_space_index.linear_independent K V).mono hst⟩
   · rintro ⟨s, rfl, si⟩
-    exact cardinal_le_rank_of_linearIndependent si
+    exact LinearIndependent.cardinal_le_rank si
 #align le_rank_iff_exists_linear_independent le_rank_iff_exists_linearIndependent
 -/
 
@@ -1681,7 +1681,7 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'}
   · rintro ⟨s, hsc, si⟩
     have : LinearIndependent K fun x : s => f.range_restrict x :=
       LinearIndependent.of_comp f.range.subtype (by convert si)
-    convert cardinal_le_rank_of_linearIndependent this.image
+    convert LinearIndependent.cardinal_le_rank this.image
     rw [← Cardinal.lift_inj, ← hsc, Cardinal.mk_image_eq_of_injOn_lift]
     exact inj_on_iff_injective.2 this.injective
 #align linear_map.le_rank_iff_exists_linear_independent LinearMap.le_rank_iff_exists_linearIndependent

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

@@ -782,13 +782,13 @@ theorem linearIndependent_le_span_aux' {ι : Type _} [Fintype ι] (v : ι → M)
 #align linear_independent_le_span_aux' linearIndependent_le_span_aux'
 -/
 
-#print linearIndependentFintypeOfLeSpanFintype /-
+#print LinearIndependent.finite_of_le_span_finite /-
 /-- If `R` satisfies the strong rank condition,
 then any linearly independent family `v : ι → M`
 contained in the span of some finite `w : set M`,
 is itself finite.
 -/
-def linearIndependentFintypeOfLeSpanFintype {ι : Type _} (v : ι → M) (i : LinearIndependent R v)
+def LinearIndependent.finite_of_le_span_finite {ι : Type _} (v : ι → M) (i : LinearIndependent R v)
     (w : Set M) [Fintype w] (s : range v ≤ span R w) : Fintype ι :=
   fintypeOfFinsetCardLe (Fintype.card w) fun t =>
     by
@@ -796,7 +796,7 @@ def linearIndependentFintypeOfLeSpanFintype {ι : Type _} (v : ι → M) (i : Li
     have i' : LinearIndependent R v' := i.comp _ Subtype.val_injective
     have s' : range v' ≤ span R w := (range_comp_subset_range _ _).trans s
     simpa using linearIndependent_le_span_aux' v' i' w s'
-#align linear_independent_fintype_of_le_span_fintype linearIndependentFintypeOfLeSpanFintype
+#align linear_independent_fintype_of_le_span_fintype LinearIndependent.finite_of_le_span_finite
 -/
 
 #print linearIndependent_le_span' /-
@@ -808,7 +808,7 @@ the cardinality of `ι` is bounded by the cardinality of `w`.
 theorem linearIndependent_le_span' {ι : Type _} (v : ι → M) (i : LinearIndependent R v) (w : Set M)
     [Fintype w] (s : range v ≤ span R w) : (#ι) ≤ Fintype.card w :=
   by
-  haveI : Fintype ι := linearIndependentFintypeOfLeSpanFintype v i w s
+  haveI : Fintype ι := LinearIndependent.finite_of_le_span_finite v i w s
   rw [Cardinal.mk_fintype]
   simp only [Cardinal.natCast_le]
   exact linearIndependent_le_span_aux' v i w s
@@ -853,7 +853,7 @@ theorem linearIndependent_le_infinite_basis {ι : Type _} (b : Basis ι R M) [In
   have i' : LinearIndependent R v' := i.comp _ Subtype.val_injective
   have w' : Fintype (Φ ⁻¹' {s}) :=
     by
-    apply linearIndependentFintypeOfLeSpanFintype v' i' (s.image b)
+    apply LinearIndependent.finite_of_le_span_finite v' i' (s.image b)
     rintro m ⟨⟨p, ⟨rfl⟩⟩, rfl⟩
     simp only [SetLike.mem_coe, Subtype.coe_mk, Finset.coe_image]
     apply Basis.mem_span_repr_support

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

@@ -201,7 +201,7 @@ theorem rank_map_le (f : M →ₗ[R] M₁) (p : Submodule R M) :
 #print rank_le_of_submodule /-
 theorem rank_le_of_submodule (s t : Submodule R M) (h : s ≤ t) :
     Module.rank R s ≤ Module.rank R t :=
-  (ofLe h).rank_le_of_injective fun ⟨x, hx⟩ ⟨y, hy⟩ eq =>
+  (inclusion h).rank_le_of_injective fun ⟨x, hx⟩ ⟨y, hy⟩ eq =>
     Subtype.eq <| show x = y from Subtype.ext_iff_val.1 Eq
 #align rank_le_of_submodule rank_le_of_submodule
 -/
@@ -966,7 +966,7 @@ theorem Basis.card_le_card_of_submodule (N : Submodule R M) [Fintype ι] (b : Ba
 theorem Basis.card_le_card_of_le {N O : Submodule R M} (hNO : N ≤ O) [Fintype ι] (b : Basis ι R O)
     [Fintype ι'] (b' : Basis ι' R N) : Fintype.card ι' ≤ Fintype.card ι :=
   b.card_le_card_of_linearIndependent
-    (b'.LinearIndependent.map' (Submodule.ofLe hNO) (N.ker_ofLe O _))
+    (b'.LinearIndependent.map' (Submodule.inclusion hNO) (N.ker_inclusion O _))
 #align basis.card_le_card_of_le Basis.card_le_card_of_le
 -/
 
@@ -1365,13 +1365,14 @@ theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd
 theorem Submodule.rank_sup_add_rank_inf_eq (s t : Submodule K V) :
     Module.rank K (s ⊔ t : Submodule K V) + Module.rank K (s ⊓ t : Submodule K V) =
       Module.rank K s + Module.rank K t :=
-  rank_add_rank_split (ofLe le_sup_left) (ofLe le_sup_right) (ofLe inf_le_left) (ofLe inf_le_right)
+  rank_add_rank_split (inclusion le_sup_left) (inclusion le_sup_right) (inclusion inf_le_left)
+    (inclusion inf_le_right)
     (by
       rw [← map_le_map_iff' (ker_subtype <| s ⊔ t), Submodule.map_sup, Submodule.map_top, ←
         LinearMap.range_comp, ← LinearMap.range_comp, subtype_comp_of_le, subtype_comp_of_le,
         range_subtype, range_subtype, range_subtype]
       exact le_rfl)
-    (ker_ofLe _ _ _) (by ext ⟨x, hx⟩; rfl)
+    (ker_inclusion _ _ _) (by ext ⟨x, hx⟩; rfl)
     (by
       rintro ⟨b₁, hb₁⟩ ⟨b₂, hb₂⟩ eq
       obtain rfl : b₁ = b₂ := congr_arg Subtype.val Eq

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

@@ -428,7 +428,7 @@ theorem union_support_maximal_linearIndependent_eq_range_basis {ι : Type w} (b
   by
   -- If that's not the case,
   by_contra h
-  simp only [← Ne.def, ne_univ_iff_exists_not_mem, mem_Union, not_exists_not,
+  simp only [← Ne.def, ne_univ_iff_exists_not_mem, mem_Union, Classical.not_exists_not,
     Finsupp.mem_support_iff, Finset.mem_coe] at h 
   -- We have some basis element `b b'` which is not in the support of any of the `v i`.
   obtain ⟨b', w⟩ := h

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

@@ -3,13 +3,13 @@ Copyright (c) 2018 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 -/
-import Mathbin.Algebra.Module.BigOperators
-import Mathbin.LinearAlgebra.Dfinsupp
-import Mathbin.LinearAlgebra.FreeModule.Basic
-import Mathbin.LinearAlgebra.InvariantBasisNumber
-import Mathbin.LinearAlgebra.Isomorphisms
-import Mathbin.LinearAlgebra.StdBasis
-import Mathbin.SetTheory.Cardinal.Cofinality
+import Algebra.Module.BigOperators
+import LinearAlgebra.Dfinsupp
+import LinearAlgebra.FreeModule.Basic
+import LinearAlgebra.InvariantBasisNumber
+import LinearAlgebra.Isomorphisms
+import LinearAlgebra.StdBasis
+import SetTheory.Cardinal.Cofinality
 
 #align_import linear_algebra.dimension from "leanprover-community/mathlib"@"47a5f8186becdbc826190ced4312f8199f9db6a5"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/48a058d7e39a80ed56858505719a0b2197900999

@@ -380,7 +380,6 @@ theorem LinearIndependent.set_finite_of_isNoetherian [IsNoetherian R M] {s : Set
 #align linear_independent.set_finite_of_is_noetherian LinearIndependent.set_finite_of_isNoetherian
 -/
 
-#print basisFintypeOfFiniteSpans /-
 -- One might hope that a finite spanning set implies that any linearly independent set is finite.
 -- While this is true over a division ring
 -- (simply because any linearly independent set can be extended to a basis),
@@ -388,7 +387,7 @@ theorem LinearIndependent.set_finite_of_isNoetherian [IsNoetherian R M] {s : Set
 /--
 Over any nontrivial ring, the existence of a finite spanning set implies that any basis is finite.
 -/
-def basisFintypeOfFiniteSpans (w : Set M) [Fintype w] (s : span R w = ⊤) {ι : Type w}
+def basis_finite_of_finite_spans (w : Set M) [Fintype w] (s : span R w = ⊤) {ι : Type w}
     (b : Basis ι R M) : Fintype ι :=
   by
   -- We'll work by contradiction, assuming `ι` is infinite.
@@ -415,8 +414,7 @@ def basisFintypeOfFiniteSpans (w : Set M) [Fintype w] (s : span R w = ⊤) {ι :
   -- giving the desire contradiction.
   refine' b.linear_independent.not_mem_span_image _ k'
   exact nm
-#align basis_fintype_of_finite_spans basisFintypeOfFiniteSpans
--/
+#align basis_fintype_of_finite_spans basis_finite_of_finite_spansₓ
 
 #print union_support_maximal_linearIndependent_eq_range_basis /-
 -- From [Les familles libres maximales d'un module ont-elles le meme cardinal?][lazarus1973]
@@ -633,7 +631,7 @@ theorem mk_eq_mk_of_basis (v : Basis ι R M) (v' : Basis ι' R M) :
   cases fintypeOrInfinite ι
   · -- `v` is a finite basis, so by `basis_fintype_of_finite_spans` so is `v'`.
     haveI : Fintype (range v) := Set.fintypeRange v
-    haveI := basisFintypeOfFiniteSpans _ v.span_eq v'
+    haveI := basis_finite_of_finite_spans _ v.span_eq v'
     -- We clean up a little:
     rw [Cardinal.mk_fintype, Cardinal.mk_fintype]
     simp only [Cardinal.lift_natCast, Cardinal.natCast_inj]
@@ -707,7 +705,7 @@ theorem basis_le_span' {ι : Type _} (b : Basis ι R M) {w : Set M} [Fintype w]
     (#ι) ≤ Fintype.card w :=
   by
   haveI := nontrivial_of_invariantBasisNumber R
-  haveI := basisFintypeOfFiniteSpans w s b
+  haveI := basis_finite_of_finite_spans w s b
   rw [Cardinal.mk_fintype ι]
   simp only [Cardinal.natCast_le]
   exact Basis.le_span'' b s

mathlib commit https://github.com/leanprover-community/mathlib/commit/48a058d7e39a80ed56858505719a0b2197900999

@@ -225,11 +225,11 @@ theorem LinearEquiv.rank_eq (f : M ≃ₗ[R] M₁) : Module.rank R M = Module.ra
 #align linear_equiv.rank_eq LinearEquiv.rank_eq
 -/
 
-#print rank_eq_of_injective /-
-theorem rank_eq_of_injective (f : M →ₗ[R] M₁) (h : Injective f) :
+#print rank_range_of_injective /-
+theorem rank_range_of_injective (f : M →ₗ[R] M₁) (h : Injective f) :
     Module.rank R M = Module.rank R f.range :=
   (LinearEquiv.ofInjective f h).rank_eq
-#align rank_eq_of_injective rank_eq_of_injective
+#align rank_eq_of_injective rank_range_of_injective
 -/
 
 #print LinearEquiv.rank_map_eq /-

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

@@ -1490,7 +1490,7 @@ theorem rank_submodule_le_one_iff (s : Submodule K V) :
     simp_rw [Subtype.ext_iff, coe_smul, Submodule.coe_mk] at hr 
     exact hr
   · rintro ⟨v₀, hv₀, h⟩
-    use ⟨v₀, hv₀⟩
+    use⟨v₀, hv₀⟩
     rintro ⟨v, hv⟩
     obtain ⟨r, hr⟩ := h v hv
     use r

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

@@ -2,11 +2,6 @@
 Copyright (c) 2018 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
-
-! This file was ported from Lean 3 source module linear_algebra.dimension
-! leanprover-community/mathlib commit 47a5f8186becdbc826190ced4312f8199f9db6a5
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Module.BigOperators
 import Mathbin.LinearAlgebra.Dfinsupp
@@ -16,6 +11,8 @@ import Mathbin.LinearAlgebra.Isomorphisms
 import Mathbin.LinearAlgebra.StdBasis
 import Mathbin.SetTheory.Cardinal.Cofinality
 
+#align_import linear_algebra.dimension from "leanprover-community/mathlib"@"47a5f8186becdbc826190ced4312f8199f9db6a5"
+
 /-!
 # Dimension of modules and vector spaces
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

@@ -1084,7 +1084,7 @@ theorem rank_self : Module.rank R R = 1 := by
 
 end StrongRankCondition
 
-section Free
+section free
 
 variable [Ring K] [StrongRankCondition K]
 
@@ -1256,7 +1256,7 @@ def finDimVectorspaceEquiv (n : ℕ) (hn : Module.rank K V = n) : V ≃ₗ[K] Fi
 #align fin_dim_vectorspace_equiv finDimVectorspaceEquiv
 -/
 
-end Free
+end free
 
 section DivisionRing
 

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

@@ -97,8 +97,6 @@ section
 
 variable [Semiring K] [AddCommMonoid V] [Module K V]
 
-include K
-
 variable (K V)
 
 #print Module.rank /-
@@ -132,6 +130,7 @@ variable {M' : Type v'} [AddCommGroup M'] [Module R M']
 
 variable {M₁ : Type v} [AddCommGroup M₁] [Module R M₁]
 
+#print LinearMap.lift_rank_le_of_injective /-
 theorem LinearMap.lift_rank_le_of_injective (f : M →ₗ[R] M') (i : Injective f) :
     Cardinal.lift.{v'} (Module.rank R M) ≤ Cardinal.lift.{v} (Module.rank R M') :=
   by
@@ -143,12 +142,16 @@ theorem LinearMap.lift_rank_le_of_injective (f : M →ₗ[R] M') (i : Injective
   refine' ⟨⟨f '' s, _⟩, cardinal.lift_mk_le'.mpr ⟨(Equiv.Set.image f s i).toEmbedding⟩⟩
   exact (li.map' _ <| linear_map.ker_eq_bot.mpr i).image
 #align linear_map.lift_rank_le_of_injective LinearMap.lift_rank_le_of_injective
+-/
 
+#print LinearMap.rank_le_of_injective /-
 theorem LinearMap.rank_le_of_injective (f : M →ₗ[R] M₁) (i : Injective f) :
     Module.rank R M ≤ Module.rank R M₁ :=
   Cardinal.lift_le.1 (f.lift_rank_le_of_injective i)
 #align linear_map.rank_le_of_injective LinearMap.rank_le_of_injective
+-/
 
+#print rank_le /-
 theorem rank_le {n : ℕ}
     (H : ∀ s : Finset M, (LinearIndependent R fun i : s => (i : M)) → s.card ≤ n) :
     Module.rank R M ≤ n := by
@@ -157,6 +160,7 @@ theorem rank_le {n : ℕ}
   rintro ⟨s, li⟩
   exact linearIndependent_bounded_of_finset_linearIndependent_bounded H _ li
 #align rank_le rank_le
+-/
 
 #print lift_rank_range_le /-
 theorem lift_rank_range_le (f : M →ₗ[R] M') :
@@ -197,11 +201,13 @@ theorem rank_map_le (f : M →ₗ[R] M₁) (p : Submodule R M) :
 #align rank_map_le rank_map_le
 -/
 
+#print rank_le_of_submodule /-
 theorem rank_le_of_submodule (s t : Submodule R M) (h : s ≤ t) :
     Module.rank R s ≤ Module.rank R t :=
   (ofLe h).rank_le_of_injective fun ⟨x, hx⟩ ⟨y, hy⟩ eq =>
     Subtype.eq <| show x = y from Subtype.ext_iff_val.1 Eq
 #align rank_le_of_submodule rank_le_of_submodule
+-/
 
 #print LinearEquiv.lift_rank_eq /-
 /-- Two linearly equivalent vector spaces have the same dimension, a version with different
@@ -222,10 +228,12 @@ theorem LinearEquiv.rank_eq (f : M ≃ₗ[R] M₁) : Module.rank R M = Module.ra
 #align linear_equiv.rank_eq LinearEquiv.rank_eq
 -/
 
+#print rank_eq_of_injective /-
 theorem rank_eq_of_injective (f : M →ₗ[R] M₁) (h : Injective f) :
     Module.rank R M = Module.rank R f.range :=
   (LinearEquiv.ofInjective f h).rank_eq
 #align rank_eq_of_injective rank_eq_of_injective
+-/
 
 #print LinearEquiv.rank_map_eq /-
 /-- Pushforwards of submodules along a `linear_equiv` have the same dimension. -/
@@ -237,18 +245,22 @@ theorem LinearEquiv.rank_map_eq (f : M ≃ₗ[R] M₁) (p : Submodule R M) :
 
 variable (R M)
 
+#print rank_top /-
 @[simp]
 theorem rank_top : Module.rank R (⊤ : Submodule R M) = Module.rank R M :=
   by
   have : (⊤ : Submodule R M) ≃ₗ[R] M := LinearEquiv.ofTop ⊤ rfl
   rw [this.rank_eq]
 #align rank_top rank_top
+-/
 
 variable {R M}
 
+#print rank_range_of_surjective /-
 theorem rank_range_of_surjective (f : M →ₗ[R] M') (h : Surjective f) :
     Module.rank R f.range = Module.rank R M' := by rw [LinearMap.range_eq_top.2 h, rank_top]
 #align rank_range_of_surjective rank_range_of_surjective
+-/
 
 #print rank_submodule_le /-
 theorem rank_submodule_le (s : Submodule R M) : Module.rank R s ≤ Module.rank R M :=
@@ -258,12 +270,14 @@ theorem rank_submodule_le (s : Submodule R M) : Module.rank R s ≤ Module.rank
 #align rank_submodule_le rank_submodule_le
 -/
 
+#print LinearMap.rank_le_of_surjective /-
 theorem LinearMap.rank_le_of_surjective (f : M →ₗ[R] M₁) (h : Surjective f) :
     Module.rank R M₁ ≤ Module.rank R M :=
   by
   rw [← rank_range_of_surjective f h]
   apply rank_range_le
 #align linear_map.rank_le_of_surjective LinearMap.rank_le_of_surjective
+-/
 
 #print rank_quotient_le /-
 theorem rank_quotient_le (p : Submodule R M) : Module.rank R (M ⧸ p) ≤ Module.rank R M :=
@@ -273,6 +287,7 @@ theorem rank_quotient_le (p : Submodule R M) : Module.rank R (M ⧸ p) ≤ Modul
 
 variable [Nontrivial R]
 
+#print cardinal_lift_le_rank_of_linearIndependent /-
 theorem cardinal_lift_le_rank_of_linearIndependent.{m} {ι : Type w} {v : ι → M}
     (hv : LinearIndependent R v) :
     Cardinal.lift.{max v m} (#ι) ≤ Cardinal.lift.{max w m} (Module.rank R M) :=
@@ -285,6 +300,7 @@ theorem cardinal_lift_le_rank_of_linearIndependent.{m} {ι : Type w} {v : ι →
     exact le_ciSup (Cardinal.bddAbove_range.{v, v} _) ⟨range v, hv.coe_range⟩
     exact le_rfl
 #align cardinal_lift_le_rank_of_linear_independent cardinal_lift_le_rank_of_linearIndependent
+-/
 
 #print cardinal_lift_le_rank_of_linearIndependent' /-
 theorem cardinal_lift_le_rank_of_linearIndependent' {ι : Type w} {v : ι → M}
@@ -309,6 +325,7 @@ theorem cardinal_le_rank_of_linearIndependent' {s : Set M}
 
 variable (R M)
 
+#print rank_punit /-
 @[simp]
 theorem rank_punit : Module.rank R PUnit = 0 :=
   by
@@ -323,20 +340,25 @@ theorem rank_punit : Module.rank R PUnit = 0 :=
   obtain ⟨a, ha⟩ := nonempty_iff_ne_empty.2 h
   simpa using LinearIndependent.ne_zero (⟨a, ha⟩ : s) li
 #align rank_punit rank_punit
+-/
 
+#print rank_bot /-
 @[simp]
 theorem rank_bot : Module.rank R (⊥ : Submodule R M) = 0 :=
   by
   have : (⊥ : Submodule R M) ≃ₗ[R] PUnit := bot_equiv_punit
   rw [this.rank_eq, rank_punit]
 #align rank_bot rank_bot
+-/
 
 variable {R M}
 
+#print exists_mem_ne_zero_of_rank_pos /-
 theorem exists_mem_ne_zero_of_rank_pos {s : Submodule R M} (h : 0 < Module.rank R s) :
     ∃ b : M, b ∈ s ∧ b ≠ 0 :=
   exists_mem_ne_zero_of_ne_bot fun eq => by rw [Eq, rank_bot] at h  <;> exact lt_irrefl _ h
 #align exists_mem_ne_zero_of_rank_pos exists_mem_ne_zero_of_rank_pos
+-/
 
 #print LinearIndependent.finite_of_isNoetherian /-
 /-- A linearly-independent family of vectors in a module over a non-trivial ring must be finite if
@@ -361,6 +383,7 @@ theorem LinearIndependent.set_finite_of_isNoetherian [IsNoetherian R M] {s : Set
 #align linear_independent.set_finite_of_is_noetherian LinearIndependent.set_finite_of_isNoetherian
 -/
 
+#print basisFintypeOfFiniteSpans /-
 -- One might hope that a finite spanning set implies that any linearly independent set is finite.
 -- While this is true over a division ring
 -- (simply because any linearly independent set can be extended to a basis),
@@ -396,7 +419,9 @@ def basisFintypeOfFiniteSpans (w : Set M) [Fintype w] (s : span R w = ⊤) {ι :
   refine' b.linear_independent.not_mem_span_image _ k'
   exact nm
 #align basis_fintype_of_finite_spans basisFintypeOfFiniteSpans
+-/
 
+#print union_support_maximal_linearIndependent_eq_range_basis /-
 -- From [Les familles libres maximales d'un module ont-elles le meme cardinal?][lazarus1973]
 /-- Over any ring `R`, if `b` is a basis for a module `M`,
 and `s` is a maximal linearly independent set,
@@ -465,6 +490,7 @@ theorem union_support_maximal_linearIndependent_eq_range_basis {ι : Type w} (b
   specialize m (range v') i' r
   exact r'' m
 #align union_support_maximal_linear_independent_eq_range_basis union_support_maximal_linearIndependent_eq_range_basis
+-/
 
 #print infinite_basis_le_maximal_linearIndependent' /-
 /-- Over any ring `R`, if `b` is an infinite basis for a module `M`,
@@ -498,6 +524,7 @@ theorem infinite_basis_le_maximal_linearIndependent {ι : Type w} (b : Basis ι
 #align infinite_basis_le_maximal_linear_independent infinite_basis_le_maximal_linearIndependent
 -/
 
+#print CompleteLattice.Independent.subtype_ne_bot_le_rank /-
 theorem CompleteLattice.Independent.subtype_ne_bot_le_rank [NoZeroSMulDivisors R M]
     {V : ι → Submodule R M} (hV : CompleteLattice.Independent V) :
     Cardinal.lift.{v} (#{ i : ι // V i ≠ ⊥ }) ≤ Cardinal.lift.{w} (Module.rank R M) :=
@@ -511,6 +538,7 @@ theorem CompleteLattice.Independent.subtype_ne_bot_le_rank [NoZeroSMulDivisors R
   have : LinearIndependent R v := (hV.comp Subtype.coe_injective).LinearIndependent _ hvV hv
   exact cardinal_lift_le_rank_of_linearIndependent' this
 #align complete_lattice.independent.subtype_ne_bot_le_rank CompleteLattice.Independent.subtype_ne_bot_le_rank
+-/
 
 end
 
@@ -542,6 +570,7 @@ theorem rank_subsingleton [Subsingleton R] : Module.rank R M = 1 :=
 
 variable [NoZeroSMulDivisors R M]
 
+#print rank_pos /-
 theorem rank_pos [Nontrivial M] : 0 < Module.rank R M :=
   by
   obtain ⟨x, hx⟩ := exists_ne (0 : M)
@@ -551,9 +580,11 @@ theorem rank_pos [Nontrivial M] : 0 < Module.rank R M :=
     simpa using cardinal_le_rank_of_linearIndependent this
   exact linearIndependent_singleton hx
 #align rank_pos rank_pos
+-/
 
 variable [Nontrivial R]
 
+#print rank_zero_iff_forall_zero /-
 theorem rank_zero_iff_forall_zero : Module.rank R M = 0 ↔ ∀ x : M, x = 0 :=
   by
   refine' ⟨fun h => _, fun h => _⟩
@@ -564,21 +595,28 @@ theorem rank_zero_iff_forall_zero : Module.rank R M = 0 ↔ ∀ x : M, x = 0 :=
   · have : (⊤ : Submodule R M) = ⊥ := by ext x; simp [h x]
     rw [← rank_top, this, rank_bot]
 #align rank_zero_iff_forall_zero rank_zero_iff_forall_zero
+-/
 
+#print rank_zero_iff /-
 /-- See `rank_subsingleton` for the reason that `nontrivial R` is needed. -/
 theorem rank_zero_iff : Module.rank R M = 0 ↔ Subsingleton M :=
   rank_zero_iff_forall_zero.trans (subsingleton_iff_forall_eq 0).symm
 #align rank_zero_iff rank_zero_iff
+-/
 
+#print rank_pos_iff_exists_ne_zero /-
 theorem rank_pos_iff_exists_ne_zero : 0 < Module.rank R M ↔ ∃ x : M, x ≠ 0 :=
   by
   rw [← not_iff_not]
   simpa using rank_zero_iff_forall_zero
 #align rank_pos_iff_exists_ne_zero rank_pos_iff_exists_ne_zero
+-/
 
+#print rank_pos_iff_nontrivial /-
 theorem rank_pos_iff_nontrivial : 0 < Module.rank R M ↔ Nontrivial M :=
   rank_pos_iff_exists_ne_zero.trans (nontrivial_iff_exists_ne 0).symm
 #align rank_pos_iff_nontrivial rank_pos_iff_nontrivial
+-/
 
 end RankZero
 
@@ -619,11 +657,13 @@ theorem mk_eq_mk_of_basis (v : Basis ι R M) (v' : Basis ι' R M) :
 #align mk_eq_mk_of_basis mk_eq_mk_of_basis
 -/
 
+#print Basis.indexEquiv /-
 /-- Given two bases indexed by `ι` and `ι'` of an `R`-module, where `R` satisfies the invariant
 basis number property, an equiv `ι ≃ ι' `. -/
 def Basis.indexEquiv (v : Basis ι R M) (v' : Basis ι' R M) : ι ≃ ι' :=
   Nonempty.some (Cardinal.lift_mk_eq.1 (Cardinal.lift_umax_eq.2 (mk_eq_mk_of_basis v v')))
 #align basis.index_equiv Basis.indexEquiv
+-/
 
 #print mk_eq_mk_of_basis' /-
 theorem mk_eq_mk_of_basis' {ι' : Type w} (v : Basis ι R M) (v' : Basis ι' R M) : (#ι) = (#ι') :=
@@ -639,6 +679,7 @@ variable {R : Type u} [Ring R] [RankCondition R]
 
 variable {M : Type v} [AddCommGroup M] [Module R M]
 
+#print Basis.le_span'' /-
 /-- An auxiliary lemma for `basis.le_span`.
 
 If `R` satisfies the rank condition,
@@ -658,7 +699,9 @@ theorem Basis.le_span'' {ι : Type _} [Fintype ι] (b : Basis ι R M) {w : Set M
     rw [← LinearMap.range_eq_top, Finsupp.range_total]
     simpa using s
 #align basis.le_span'' Basis.le_span''
+-/
 
+#print basis_le_span' /-
 /--
 Another auxiliary lemma for `basis.le_span`, which does not require assuming the basis is finite,
 but still assumes we have a finite spanning set.
@@ -672,7 +715,9 @@ theorem basis_le_span' {ι : Type _} (b : Basis ι R M) {w : Set M} [Fintype w]
   simp only [Cardinal.natCast_le]
   exact Basis.le_span'' b s
 #align basis_le_span' basis_le_span'
+-/
 
+#print Basis.le_span /-
 -- Note that if `R` satisfies the strong rank condition,
 -- this also follows from `linear_independent_le_span` below.
 /-- If `R` satisfies the rank condition,
@@ -708,6 +753,7 @@ theorem Basis.le_span {J : Set M} (v : Basis ι R M) (hJ : span R J = ⊤) : (#r
     · exact fun j => (Cardinal.lt_aleph0_of_finite _).le
     · simpa
 #align basis.le_span Basis.le_span
+-/
 
 end RankCondition
 
@@ -719,6 +765,7 @@ variable {M : Type v} [AddCommGroup M] [Module R M]
 
 open Submodule
 
+#print linearIndependent_le_span_aux' /-
 -- An auxiliary lemma for `linear_independent_le_span'`,
 -- with the additional assumption that the linearly independent family is finite.
 theorem linearIndependent_le_span_aux' {ι : Type _} [Fintype ι] (v : ι → M)
@@ -738,6 +785,7 @@ theorem linearIndependent_le_span_aux' {ι : Type _} [Fintype ι] (v : ι → M)
     rw [← sub_eq_zero, ← LinearMap.map_sub] at h 
     exact sub_eq_zero.mp (linear_independent_iff.mp i _ h)
 #align linear_independent_le_span_aux' linearIndependent_le_span_aux'
+-/
 
 #print linearIndependentFintypeOfLeSpanFintype /-
 /-- If `R` satisfies the strong rank condition,
@@ -756,6 +804,7 @@ def linearIndependentFintypeOfLeSpanFintype {ι : Type _} (v : ι → M) (i : Li
 #align linear_independent_fintype_of_le_span_fintype linearIndependentFintypeOfLeSpanFintype
 -/
 
+#print linearIndependent_le_span' /-
 /-- If `R` satisfies the strong rank condition,
 then for any linearly independent family `v : ι → M`
 contained in the span of some finite `w : set M`,
@@ -769,7 +818,9 @@ theorem linearIndependent_le_span' {ι : Type _} (v : ι → M) (i : LinearIndep
   simp only [Cardinal.natCast_le]
   exact linearIndependent_le_span_aux' v i w s
 #align linear_independent_le_span' linearIndependent_le_span'
+-/
 
+#print linearIndependent_le_span /-
 /-- If `R` satisfies the strong rank condition,
 then for any linearly independent family `v : ι → M`
 and any finite spanning set `w : set M`,
@@ -782,13 +833,17 @@ theorem linearIndependent_le_span {ι : Type _} (v : ι → M) (i : LinearIndepe
   rw [s]
   exact le_top
 #align linear_independent_le_span linearIndependent_le_span
+-/
 
+#print linearIndependent_le_span_finset /-
 /-- A version of `linear_independent_le_span` for `finset`. -/
 theorem linearIndependent_le_span_finset {ι : Type _} (v : ι → M) (i : LinearIndependent R v)
     (w : Finset M) (s : span R (w : Set M) = ⊤) : (#ι) ≤ w.card := by
   simpa only [Finset.coe_sort_coe, Fintype.card_coe] using linearIndependent_le_span v i w s
 #align linear_independent_le_span_finset linearIndependent_le_span_finset
+-/
 
+#print linearIndependent_le_infinite_basis /-
 /-- An auxiliary lemma for `linear_independent_le_basis`:
 we handle the case where the basis `b` is infinite.
 -/
@@ -809,7 +864,9 @@ theorem linearIndependent_le_infinite_basis {ι : Type _} (b : Basis ι R M) [In
     apply Basis.mem_span_repr_support
   exact w.false
 #align linear_independent_le_infinite_basis linearIndependent_le_infinite_basis
+-/
 
+#print linearIndependent_le_basis /-
 /-- Over any ring `R` satisfying the strong rank condition,
 if `b` is a basis for a module `M`,
 and `s` is a linearly independent set,
@@ -829,6 +886,7 @@ theorem linearIndependent_le_basis {ι : Type _} (b : Basis ι R M) {κ : Type _
   ·-- and otherwise we have `linear_indepedent_le_infinite_basis`.
     exact linearIndependent_le_infinite_basis b v i
 #align linear_independent_le_basis linearIndependent_le_basis
+-/
 
 #print Basis.card_le_card_of_linearIndependent_aux /-
 /-- In an `n`-dimensional space, the rank is at most `m`. -/
@@ -838,6 +896,7 @@ theorem Basis.card_le_card_of_linearIndependent_aux {R : Type _} [Ring R] [Stron
 #align basis.card_le_card_of_linear_independent_aux Basis.card_le_card_of_linearIndependent_aux
 -/
 
+#print maximal_linearIndependent_eq_infinite_basis /-
 -- When the basis is not infinite this need not be true!
 /-- Over any ring `R` satisfying the strong rank condition,
 if `b` is an infinite basis for a module `M`,
@@ -854,6 +913,7 @@ theorem maximal_linearIndependent_eq_infinite_basis {ι : Type _} (b : Basis ι
   · haveI : Nontrivial R := nontrivial_of_invariantBasisNumber R
     exact infinite_basis_le_maximal_linearIndependent b v i m
 #align maximal_linear_independent_eq_infinite_basis maximal_linearIndependent_eq_infinite_basis
+-/
 
 #print Basis.mk_eq_rank'' /-
 theorem Basis.mk_eq_rank'' {ι : Type v} (v : Basis ι R M) : (#ι) = Module.rank R M :=
@@ -878,6 +938,7 @@ theorem Basis.mk_range_eq_rank (v : Basis ι R M) : (#range v) = Module.rank R M
 #align basis.mk_range_eq_rank Basis.mk_range_eq_rank
 -/
 
+#print rank_eq_card_basis /-
 /-- If a vector space has a finite basis, then its dimension (seen as a cardinal) is equal to the
 cardinality of the basis. -/
 theorem rank_eq_card_basis {ι : Type w} [Fintype ι] (h : Basis ι R M) :
@@ -886,7 +947,9 @@ theorem rank_eq_card_basis {ι : Type w} [Fintype ι] (h : Basis ι R M) :
   haveI := nontrivial_of_invariantBasisNumber R
   rw [← h.mk_range_eq_rank, Cardinal.mk_fintype, Set.card_range_of_injective h.injective]
 #align rank_eq_card_basis rank_eq_card_basis
+-/
 
+#print Basis.card_le_card_of_linearIndependent /-
 theorem Basis.card_le_card_of_linearIndependent {ι : Type _} [Fintype ι] (b : Basis ι R M)
     {ι' : Type _} [Fintype ι'] {v : ι' → M} (hv : LinearIndependent R v) :
     Fintype.card ι' ≤ Fintype.card ι :=
@@ -895,6 +958,7 @@ theorem Basis.card_le_card_of_linearIndependent {ι : Type _} [Fintype ι] (b :
   simpa [rank_eq_card_basis b, Cardinal.mk_fintype] using
     cardinal_lift_le_rank_of_linearIndependent' hv
 #align basis.card_le_card_of_linear_independent Basis.card_le_card_of_linearIndependent
+-/
 
 #print Basis.card_le_card_of_submodule /-
 theorem Basis.card_le_card_of_submodule (N : Submodule R M) [Fintype ι] (b : Basis ι R M)
@@ -903,11 +967,13 @@ theorem Basis.card_le_card_of_submodule (N : Submodule R M) [Fintype ι] (b : Ba
 #align basis.card_le_card_of_submodule Basis.card_le_card_of_submodule
 -/
 
+#print Basis.card_le_card_of_le /-
 theorem Basis.card_le_card_of_le {N O : Submodule R M} (hNO : N ≤ O) [Fintype ι] (b : Basis ι R O)
     [Fintype ι'] (b' : Basis ι' R N) : Fintype.card ι' ≤ Fintype.card ι :=
   b.card_le_card_of_linearIndependent
     (b'.LinearIndependent.map' (Submodule.ofLe hNO) (N.ker_ofLe O _))
 #align basis.card_le_card_of_le Basis.card_le_card_of_le
+-/
 
 #print Basis.mk_eq_rank /-
 theorem Basis.mk_eq_rank (v : Basis ι R M) :
@@ -925,12 +991,14 @@ theorem Basis.mk_eq_rank'.{m} (v : Basis ι R M) :
 #align basis.mk_eq_rank' Basis.mk_eq_rank'
 -/
 
+#print Basis.nonempty_fintype_index_of_rank_lt_aleph0 /-
 /-- If a module has a finite dimension, all bases are indexed by a finite type. -/
 theorem Basis.nonempty_fintype_index_of_rank_lt_aleph0 {ι : Type _} (b : Basis ι R M)
     (h : Module.rank R M < ℵ₀) : Nonempty (Fintype ι) := by
   rwa [← Cardinal.lift_lt, ← b.mk_eq_rank, Cardinal.lift_aleph0, Cardinal.lift_lt_aleph0,
     Cardinal.lt_aleph0_iff_fintype] at h 
 #align basis.nonempty_fintype_index_of_rank_lt_aleph_0 Basis.nonempty_fintype_index_of_rank_lt_aleph0
+-/
 
 #print Basis.fintypeIndexOfRankLtAleph0 /-
 /-- If a module has a finite dimension, all bases are indexed by a finite type. -/
@@ -940,11 +1008,13 @@ noncomputable def Basis.fintypeIndexOfRankLtAleph0 {ι : Type _} (b : Basis ι R
 #align basis.fintype_index_of_rank_lt_aleph_0 Basis.fintypeIndexOfRankLtAleph0
 -/
 
+#print Basis.finite_index_of_rank_lt_aleph0 /-
 /-- If a module has a finite dimension, all bases are indexed by a finite set. -/
 theorem Basis.finite_index_of_rank_lt_aleph0 {ι : Type _} {s : Set ι} (b : Basis s R M)
     (h : Module.rank R M < ℵ₀) : s.Finite :=
   finite_def.2 (b.nonempty_fintype_index_of_rank_lt_aleph0 h)
 #align basis.finite_index_of_rank_lt_aleph_0 Basis.finite_index_of_rank_lt_aleph0
+-/
 
 #print rank_span /-
 theorem rank_span {v : ι → M} (hv : LinearIndependent R v) :
@@ -963,6 +1033,7 @@ theorem rank_span_set {s : Set M} (hs : LinearIndependent R (fun x => x : s →
 #align rank_span_set rank_span_set
 -/
 
+#print Submodule.inductionOnRank /-
 /-- If `N` is a submodule in a free, finitely generated module,
 do induction on adjoining a linear independent element to a submodule. -/
 def Submodule.inductionOnRank [IsDomain R] [Fintype ι] (b : Basis ι R M)
@@ -974,7 +1045,9 @@ def Submodule.inductionOnRank [IsDomain R] [Fintype ι] (b : Basis ι R M)
   Submodule.inductionOnRankAux b P ih (Fintype.card ι) N fun s hs hli => by
     simpa using b.card_le_card_of_linear_independent hli
 #align submodule.induction_on_rank Submodule.inductionOnRank
+-/
 
+#print Ideal.rank_eq /-
 /-- If `S` a finite-dimensional ring extension of `R` which is free as an `R`-module,
 then the rank of an ideal `I` of `S` over `R` is the same as the rank of `S`.
 -/
@@ -998,6 +1071,7 @@ theorem Ideal.rank_eq {R S : Type _} [CommRing R] [StrongRankCondition R] [Ring
           (linear_map.ker_eq_bot.mpr Subtype.coe_injective)))
       (c.card_le_card_of_linear_independent this)
 #align ideal.rank_eq Ideal.rank_eq
+-/
 
 variable (R)
 
@@ -1100,6 +1174,7 @@ theorem LinearEquiv.nonempty_equiv_iff_rank_eq :
 #align linear_equiv.nonempty_equiv_iff_rank_eq LinearEquiv.nonempty_equiv_iff_rank_eq
 -/
 
+#print rank_prod /-
 /-- The rank of `M × N` is `(module.rank R M).lift + (module.rank R N).lift`. -/
 @[simp]
 theorem rank_prod :
@@ -1109,11 +1184,14 @@ theorem rank_prod :
   simpa [rank_eq_card_choose_basis_index K V, rank_eq_card_choose_basis_index K V', lift_umax,
     lift_umax'] using ((choose_basis K V).Prod (choose_basis K V')).mk_eq_rank.symm
 #align rank_prod rank_prod
+-/
 
+#print rank_prod' /-
 /-- If `M` and `N` lie in the same universe, the rank of `M × N` is
   `(module.rank R M) + (module.rank R N)`. -/
 theorem rank_prod' : Module.rank K (V × V₁) = Module.rank K V + Module.rank K V₁ := by simp
 #align rank_prod' rank_prod'
+-/
 
 section Fintype
 
@@ -1121,6 +1199,7 @@ variable [∀ i, AddCommGroup (φ i)] [∀ i, Module K (φ i)] [∀ i, Module.Fr
 
 open LinearMap
 
+#print rank_pi /-
 /-- The rank of a finite product is the sum of the ranks. -/
 @[simp]
 theorem rank_pi [Finite η] : Module.rank K (∀ i, φ i) = Cardinal.sum fun i => Module.rank K (φ i) :=
@@ -1130,29 +1209,39 @@ theorem rank_pi [Finite η] : Module.rank K (∀ i, φ i) = Cardinal.sum fun i =
   let b : Basis _ K (∀ i, φ i) := Pi.basis fun i => B i
   simp [← b.mk_eq_rank'', fun i => (B i).mk_eq_rank'']
 #align rank_pi rank_pi
+-/
 
 variable [Fintype η]
 
+#print rank_fun /-
 theorem rank_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] [Module.Free K V] :
     Module.rank K (η → V) = Fintype.card η * Module.rank K V := by
   rw [rank_pi, Cardinal.sum_const', Cardinal.mk_fintype]
 #align rank_fun rank_fun
+-/
 
+#print rank_fun_eq_lift_mul /-
 theorem rank_fun_eq_lift_mul :
     Module.rank K (η → V) =
       (Fintype.card η : Cardinal.{max u₁' v}) * Cardinal.lift.{u₁'} (Module.rank K V) :=
   by rw [rank_pi, Cardinal.sum_const, Cardinal.mk_fintype, Cardinal.lift_natCast]
 #align rank_fun_eq_lift_mul rank_fun_eq_lift_mul
+-/
 
+#print rank_fun' /-
 theorem rank_fun' : Module.rank K (η → K) = Fintype.card η := by
   rw [rank_fun_eq_lift_mul, rank_self, Cardinal.lift_one, mul_one, Cardinal.natCast_inj]
 #align rank_fun' rank_fun'
+-/
 
+#print rank_fin_fun /-
 theorem rank_fin_fun (n : ℕ) : Module.rank K (Fin n → K) = n := by simp [rank_fun']
 #align rank_fin_fun rank_fin_fun
+-/
 
 end Fintype
 
+#print finDimVectorspaceEquiv /-
 -- TODO: merge with the `finrank` content
 /-- An `n`-dimensional `K`-vector space is equivalent to `fin n → K`. -/
 def finDimVectorspaceEquiv (n : ℕ) (hn : Module.rank K V = n) : V ≃ₗ[K] Fin n → K :=
@@ -1165,6 +1254,7 @@ def finDimVectorspaceEquiv (n : ℕ) (hn : Module.rank K V = n) : V ≃ₗ[K] Fi
   haveI : Module.Free K (Fin n → K) := Module.Free.pi _ _
   exact Classical.choice (nonempty_linearEquiv_of_lift_rank_eq hn)
 #align fin_dim_vectorspace_equiv finDimVectorspaceEquiv
+-/
 
 end Free
 
@@ -1209,13 +1299,16 @@ theorem rank_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V
 #align rank_span_of_finset rank_span_of_finset
 -/
 
+#print rank_quotient_add_rank /-
 theorem rank_quotient_add_rank (p : Submodule K V) :
     Module.rank K (V ⧸ p) + Module.rank K p = Module.rank K V := by
   classical exact
     let ⟨f⟩ := quotient_prod_linearEquiv p
     rank_prod'.symm.trans f.rank_eq
 #align rank_quotient_add_rank rank_quotient_add_rank
+-/
 
+#print rank_range_add_rank_ker /-
 /-- rank-nullity theorem -/
 theorem rank_range_add_rank_ker (f : V →ₗ[K] V₁) :
     Module.rank K f.range + Module.rank K f.ker = Module.rank K V :=
@@ -1223,11 +1316,14 @@ theorem rank_range_add_rank_ker (f : V →ₗ[K] V₁) :
   haveI := fun p : Submodule K V => Classical.decEq (V ⧸ p)
   rw [← f.quot_ker_equiv_range.rank_eq, rank_quotient_add_rank]
 #align rank_range_add_rank_ker rank_range_add_rank_ker
+-/
 
+#print rank_eq_of_surjective /-
 theorem rank_eq_of_surjective (f : V →ₗ[K] V₁) (h : Surjective f) :
     Module.rank K V = Module.rank K V₁ + Module.rank K f.ker := by
   rw [← rank_range_add_rank_ker f, ← rank_range_of_surjective f h]
 #align rank_eq_of_surjective rank_eq_of_surjective
+-/
 
 section
 
@@ -1237,6 +1333,7 @@ variable [AddCommGroup V₃] [Module K V₃]
 
 open LinearMap
 
+#print rank_add_rank_split /-
 /-- This is mostly an auxiliary lemma for `submodule.rank_sup_add_rank_inf_eq`. -/
 theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd : V₁ →ₗ[K] V₂)
     (ce : V₁ →ₗ[K] V₃) (hde : ⊤ ≤ db.range ⊔ eb.range) (hgd : ker cd = ⊥)
@@ -1267,7 +1364,9 @@ theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd
     refine' ⟨c, h₁, _⟩
     rw [h₂, _root_.neg_neg]
 #align rank_add_rank_split rank_add_rank_split
+-/
 
+#print Submodule.rank_sup_add_rank_inf_eq /-
 theorem Submodule.rank_sup_add_rank_inf_eq (s t : Submodule K V) :
     Module.rank K (s ⊔ t : Submodule K V) + Module.rank K (s ⊓ t : Submodule K V) =
       Module.rank K s + Module.rank K t :=
@@ -1283,11 +1382,14 @@ theorem Submodule.rank_sup_add_rank_inf_eq (s t : Submodule K V) :
       obtain rfl : b₁ = b₂ := congr_arg Subtype.val Eq
       exact ⟨⟨b₁, hb₁, hb₂⟩, rfl, rfl⟩)
 #align submodule.rank_sup_add_rank_inf_eq Submodule.rank_sup_add_rank_inf_eq
+-/
 
+#print Submodule.rank_add_le_rank_add_rank /-
 theorem Submodule.rank_add_le_rank_add_rank (s t : Submodule K V) :
     Module.rank K (s ⊔ t : Submodule K V) ≤ Module.rank K s + Module.rank K t := by
   rw [← Submodule.rank_sup_add_rank_inf_eq]; exact self_le_add_right _ _
 #align submodule.rank_add_le_rank_add_rank Submodule.rank_add_le_rank_add_rank
+-/
 
 end
 
@@ -1310,11 +1412,13 @@ def Basis.ofRankEqZero {ι : Type _} [IsEmpty ι] (hV : Module.rank K V = 0) : B
 #align basis.of_rank_eq_zero Basis.ofRankEqZero
 -/
 
+#print Basis.ofRankEqZero_apply /-
 @[simp]
 theorem Basis.ofRankEqZero_apply {ι : Type _} [IsEmpty ι] (hV : Module.rank K V = 0) (i : ι) :
     Basis.ofRankEqZero hV i = 0 :=
   rfl
 #align basis.of_rank_eq_zero_apply Basis.ofRankEqZero_apply
+-/
 
 #print le_rank_iff_exists_linearIndependent /-
 theorem le_rank_iff_exists_linearIndependent {c : Cardinal} :
@@ -1331,6 +1435,7 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} :
 #align le_rank_iff_exists_linear_independent le_rank_iff_exists_linearIndependent
 -/
 
+#print le_rank_iff_exists_linearIndependent_finset /-
 theorem le_rank_iff_exists_linearIndependent_finset {n : ℕ} :
     ↑n ≤ Module.rank K V ↔
       ∃ s : Finset V, s.card = n ∧ LinearIndependent K (coe : (s : Set V) → V) :=
@@ -1342,6 +1447,7 @@ theorem le_rank_iff_exists_linearIndependent_finset {n : ℕ} :
   · rintro ⟨s, rfl, si⟩
     exact ⟨s, ⟨s, rfl, rfl⟩, si⟩
 #align le_rank_iff_exists_linear_independent_finset le_rank_iff_exists_linearIndependent_finset
+-/
 
 #print rank_le_one_iff /-
 /-- A vector space has dimension at most `1` if and only if there is a
@@ -1370,6 +1476,7 @@ theorem rank_le_one_iff : Module.rank K V ≤ 1 ↔ ∃ v₀ : V, ∀ v, ∃ r :
 #align rank_le_one_iff rank_le_one_iff
 -/
 
+#print rank_submodule_le_one_iff /-
 /-- A submodule has dimension at most `1` if and only if there is a
 single vector in the submodule such that the submodule is contained in
 its span. -/
@@ -1393,7 +1500,9 @@ theorem rank_submodule_le_one_iff (s : Submodule K V) :
     simp_rw [Subtype.ext_iff, coe_smul, Submodule.coe_mk]
     exact hr
 #align rank_submodule_le_one_iff rank_submodule_le_one_iff
+-/
 
+#print rank_submodule_le_one_iff' /-
 /-- A submodule has dimension at most `1` if and only if there is a
 single vector, not necessarily in the submodule, such that the
 submodule is contained in its span. -/
@@ -1416,6 +1525,7 @@ theorem rank_submodule_le_one_iff' (s : Submodule K V) : Module.rank K s ≤ 1 
       rw [← Submodule.eq_bot_iff] at hw 
       simp [hw]
 #align rank_submodule_le_one_iff' rank_submodule_le_one_iff'
+-/
 
 #print Submodule.rank_le_one_iff_isPrincipal /-
 theorem Submodule.rank_le_one_iff_isPrincipal (W : Submodule K V) :
@@ -1433,10 +1543,12 @@ theorem Submodule.rank_le_one_iff_isPrincipal (W : Submodule K V) :
 #align submodule.rank_le_one_iff_is_principal Submodule.rank_le_one_iff_isPrincipal
 -/
 
+#print Module.rank_le_one_iff_top_isPrincipal /-
 theorem Module.rank_le_one_iff_top_isPrincipal :
     Module.rank K V ≤ 1 ↔ (⊤ : Submodule K V).IsPrincipal := by
   rw [← Submodule.rank_le_one_iff_isPrincipal, rank_top]
 #align module.rank_le_one_iff_top_is_principal Module.rank_le_one_iff_top_isPrincipal
+-/
 
 end DivisionRing
 
@@ -1472,10 +1584,12 @@ theorem rank_le_domain (f : V →ₗ[K] V₁) : rank f ≤ Module.rank K V :=
 #align linear_map.rank_le_domain LinearMap.rank_le_domain
 -/
 
+#print LinearMap.rank_zero /-
 @[simp]
 theorem rank_zero [Nontrivial K] : rank (0 : V →ₗ[K] V') = 0 := by
   rw [rank, LinearMap.range_zero, rank_bot]
 #align linear_map.rank_zero LinearMap.rank_zero
+-/
 
 variable [AddCommGroup V''] [Module K V'']
 
@@ -1495,12 +1609,14 @@ theorem lift_rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
 #align linear_map.lift_rank_comp_le_right LinearMap.lift_rank_comp_le_right
 -/
 
+#print LinearMap.lift_rank_comp_le /-
 /-- The rank of the composition of two maps is less than the minimum of their ranks. -/
 theorem lift_rank_comp_le (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
     Cardinal.lift.{v'} (rank (f.comp g)) ≤
       min (Cardinal.lift.{v'} (rank f)) (Cardinal.lift.{v''} (rank g)) :=
   le_min (Cardinal.lift_le.mpr <| rank_comp_le_left _ _) (lift_rank_comp_le_right _ _)
 #align linear_map.lift_rank_comp_le LinearMap.lift_rank_comp_le
+-/
 
 variable [AddCommGroup V'₁] [Module K V'₁]
 
@@ -1510,6 +1626,7 @@ theorem rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) : rank
 #align linear_map.rank_comp_le_right LinearMap.rank_comp_le_right
 -/
 
+#print LinearMap.rank_comp_le /-
 /-- The rank of the composition of two maps is less than the minimum of their ranks.
 
 See `lift_rank_comp_le` for the universe-polymorphic version. -/
@@ -1517,6 +1634,7 @@ theorem rank_comp_le (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) :
     rank (f.comp g) ≤ min (rank f) (rank g) := by
   simpa only [Cardinal.lift_id] using lift_rank_comp_le g f
 #align linear_map.rank_comp_le LinearMap.rank_comp_le
+-/
 
 end Ring
 
@@ -1526,6 +1644,7 @@ variable [DivisionRing K] [AddCommGroup V] [Module K V] [AddCommGroup V₁] [Mod
 
 variable [AddCommGroup V'] [Module K V']
 
+#print LinearMap.rank_add_le /-
 theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
   calc
     rank (f + g) ≤ Module.rank K (f.range ⊔ g.range : Submodule K V') :=
@@ -1538,13 +1657,17 @@ theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
               mem_sup.2 ⟨_, ⟨x, rfl⟩, _, ⟨x, rfl⟩, rfl⟩
     _ ≤ rank f + rank g := Submodule.rank_add_le_rank_add_rank _ _
 #align linear_map.rank_add_le LinearMap.rank_add_le
+-/
 
+#print LinearMap.rank_finset_sum_le /-
 theorem rank_finset_sum_le {η} (s : Finset η) (f : η → V →ₗ[K] V') :
     rank (∑ d in s, f d) ≤ ∑ d in s, rank (f d) :=
   @Finset.sum_hom_rel _ _ _ _ _ (fun a b => rank a ≤ b) f (fun d => rank (f d)) s
     (le_of_eq rank_zero) fun i g c h => le_trans (rank_add_le _ _) (add_le_add_left h _)
 #align linear_map.rank_finset_sum_le LinearMap.rank_finset_sum_le
+-/
 
+#print LinearMap.le_rank_iff_exists_linearIndependent /-
 theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'} :
     c ≤ rank f ↔
       ∃ s : Set V,
@@ -1566,7 +1689,9 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'}
     rw [← Cardinal.lift_inj, ← hsc, Cardinal.mk_image_eq_of_injOn_lift]
     exact inj_on_iff_injective.2 this.injective
 #align linear_map.le_rank_iff_exists_linear_independent LinearMap.le_rank_iff_exists_linearIndependent
+-/
 
+#print LinearMap.le_rank_iff_exists_linearIndependent_finset /-
 theorem le_rank_iff_exists_linearIndependent_finset {n : ℕ} {f : V →ₗ[K] V'} :
     ↑n ≤ rank f ↔ ∃ s : Finset V, s.card = n ∧ LinearIndependent K fun x : (s : Set V) => f x :=
   by
@@ -1578,6 +1703,7 @@ theorem le_rank_iff_exists_linearIndependent_finset {n : ℕ} {f : V →ₗ[K] V
   · rintro ⟨s, rfl, si⟩
     exact ⟨s, ⟨s, rfl, rfl⟩, si⟩
 #align linear_map.le_rank_iff_exists_linear_independent_finset LinearMap.le_rank_iff_exists_linearIndependent_finset
+-/
 
 end DivisionRing
 

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

@@ -1206,7 +1206,6 @@ theorem rank_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V
     Module.rank K (span K (↑s : Set V)) ≤ (#(↑s : Set V)) := rank_span_le ↑s
     _ = s.card := by rw [Finset.coe_sort_coe, Cardinal.mk_coe_finset]
     _ < ℵ₀ := Cardinal.nat_lt_aleph0 _
-    
 #align rank_span_of_finset rank_span_of_finset
 -/
 
@@ -1538,7 +1537,6 @@ theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
             show f x + g x ∈ (f.range ⊔ g.range : Submodule K V') from
               mem_sup.2 ⟨_, ⟨x, rfl⟩, _, ⟨x, rfl⟩, rfl⟩
     _ ≤ rank f + rank g := Submodule.rank_add_le_rank_add_rank _ _
-    
 #align linear_map.rank_add_le LinearMap.rank_add_le
 
 theorem rank_finset_sum_le {η} (s : Finset η) (f : η → V →ₗ[K] V') :

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

@@ -447,7 +447,7 @@ theorem union_support_maximal_linearIndependent_eq_range_basis {ι : Type w} (b
     have l₀ : l none = 0 := by
       rw [← eq_neg_iff_add_eq_zero] at z 
       replace z := neg_eq_iff_eq_neg.mpr z
-      apply_fun fun x => b.repr x b'  at z 
+      apply_fun fun x => b.repr x b' at z 
       simp only [repr_self, LinearEquiv.map_smul, mul_one, Finsupp.single_eq_same, Pi.neg_apply,
         Finsupp.smul_single', LinearEquiv.map_neg, Finsupp.coe_neg] at z 
       erw [Finsupp.congr_fun (Finsupp.apply_total R (b.repr : M →ₗ[R] ι →₀ R) v l.some) b'] at z 
@@ -733,7 +733,7 @@ theorem linearIndependent_le_span_aux' {ι : Type _} [Fintype ι] (v : ι → M)
   · apply Finsupp.total
     exact fun i => Span.repr R w ⟨v i, s (mem_range_self i)⟩
   · intro f g h
-    apply_fun Finsupp.total w M R coe  at h 
+    apply_fun Finsupp.total w M R coe at h 
     simp only [Finsupp.total_total, Submodule.coe_mk, Span.finsupp_total_repr] at h 
     rw [← sub_eq_zero, ← LinearMap.map_sub] at h 
     exact sub_eq_zero.mp (linear_independent_iff.mp i _ h)
@@ -1213,8 +1213,8 @@ theorem rank_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V
 theorem rank_quotient_add_rank (p : Submodule K V) :
     Module.rank K (V ⧸ p) + Module.rank K p = Module.rank K V := by
   classical exact
-      let ⟨f⟩ := quotient_prod_linearEquiv p
-      rank_prod'.symm.trans f.rank_eq
+    let ⟨f⟩ := quotient_prod_linearEquiv p
+    rank_prod'.symm.trans f.rank_eq
 #align rank_quotient_add_rank rank_quotient_add_rank
 
 /-- rank-nullity theorem -/
@@ -1413,7 +1413,7 @@ theorem rank_submodule_le_one_iff' (s : Submodule K V) : Module.rank K s ≤ 1 
         rintro rfl
         simpa using hw0
       rwa [span_singleton_smul_eq (IsUnit.mk0 _ h0) _]
-    · push_neg  at hw 
+    · push_neg at hw 
       rw [← Submodule.eq_bot_iff] at hw 
       simp [hw]
 #align rank_submodule_le_one_iff' rank_submodule_le_one_iff'

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

@@ -187,7 +187,7 @@ theorem lift_rank_map_le (f : M →ₗ[R] M') (p : Submodule R M) :
     Cardinal.lift.{v} (Module.rank R (p.map f)) ≤ Cardinal.lift.{v'} (Module.rank R p) :=
   by
   have h := lift_rank_range_le (f.comp (Submodule.subtype p))
-  rwa [LinearMap.range_comp, range_subtype] at h
+  rwa [LinearMap.range_comp, range_subtype] at h 
 #align lift_rank_map_le lift_rank_map_le
 -/
 
@@ -335,7 +335,7 @@ variable {R M}
 
 theorem exists_mem_ne_zero_of_rank_pos {s : Submodule R M} (h : 0 < Module.rank R s) :
     ∃ b : M, b ∈ s ∧ b ≠ 0 :=
-  exists_mem_ne_zero_of_ne_bot fun eq => by rw [Eq, rank_bot] at h <;> exact lt_irrefl _ h
+  exists_mem_ne_zero_of_ne_bot fun eq => by rw [Eq, rank_bot] at h  <;> exact lt_irrefl _ h
 #align exists_mem_ne_zero_of_rank_pos exists_mem_ne_zero_of_rank_pos
 
 #print LinearIndependent.finite_of_isNoetherian /-
@@ -350,7 +350,7 @@ theorem LinearIndependent.finite_of_isNoetherian [IsNoetherian R M] {v : ι →
       fun i contra => _
   apply hv.ne_zero i
   have : v i ∈ R ∙ v i := Submodule.mem_span_singleton_self (v i)
-  rwa [contra, Submodule.mem_bot] at this
+  rwa [contra, Submodule.mem_bot] at this 
 #align linear_independent.finite_of_is_noetherian LinearIndependent.finite_of_isNoetherian
 -/
 
@@ -409,7 +409,7 @@ theorem union_support_maximal_linearIndependent_eq_range_basis {ι : Type w} (b
   -- If that's not the case,
   by_contra h
   simp only [← Ne.def, ne_univ_iff_exists_not_mem, mem_Union, not_exists_not,
-    Finsupp.mem_support_iff, Finset.mem_coe] at h
+    Finsupp.mem_support_iff, Finset.mem_coe] at h 
   -- We have some basis element `b b'` which is not in the support of any of the `v i`.
   obtain ⟨b', w⟩ := h
   -- Using this, we'll construct a linearly independent family strictly larger than `v`,
@@ -425,43 +425,43 @@ theorem union_support_maximal_linearIndependent_eq_range_basis {ι : Type w} (b
   have r'' : range v ≠ range v' := by
     intro e
     have p : b b' ∈ range v' := by use none; rfl
-    rw [← e] at p
+    rw [← e] at p 
     exact r' p
   have inj' : injective v' := by
     rintro (_ | k) (_ | k) z
     · rfl
     · exfalso; exact r' ⟨k, z.symm⟩
     · exfalso; exact r' ⟨k, z⟩
-    · congr ; exact i.injective z
+    · congr; exact i.injective z
   -- The key step in the proof is checking that this strictly larger family is linearly independent.
   have i' : LinearIndependent R (coe : range v' → M) :=
     by
     rw [linearIndependent_subtype_range inj', linearIndependent_iff]
     intro l z
-    rw [Finsupp.total_option] at z
-    simp only [v', Option.elim'] at z
-    change _ + Finsupp.total κ M R v l.some = 0 at z
+    rw [Finsupp.total_option] at z 
+    simp only [v', Option.elim'] at z 
+    change _ + Finsupp.total κ M R v l.some = 0 at z 
     -- We have some linear combination of `b b'` and the `v i`, which we want to show is trivial.
     -- We'll first show the coefficient of `b b'` is zero,
     -- by expressing the `v i` in the basis `b`, and using that the `v i` have no `b b'` term.
     have l₀ : l none = 0 := by
-      rw [← eq_neg_iff_add_eq_zero] at z
+      rw [← eq_neg_iff_add_eq_zero] at z 
       replace z := neg_eq_iff_eq_neg.mpr z
-      apply_fun fun x => b.repr x b'  at z
+      apply_fun fun x => b.repr x b'  at z 
       simp only [repr_self, LinearEquiv.map_smul, mul_one, Finsupp.single_eq_same, Pi.neg_apply,
-        Finsupp.smul_single', LinearEquiv.map_neg, Finsupp.coe_neg] at z
-      erw [Finsupp.congr_fun (Finsupp.apply_total R (b.repr : M →ₗ[R] ι →₀ R) v l.some) b'] at z
+        Finsupp.smul_single', LinearEquiv.map_neg, Finsupp.coe_neg] at z 
+      erw [Finsupp.congr_fun (Finsupp.apply_total R (b.repr : M →ₗ[R] ι →₀ R) v l.some) b'] at z 
       simpa [Finsupp.total_apply, w] using z
     -- Then all the other coefficients are zero, because `v` is linear independent.
     have l₁ : l.some = 0 := by
-      rw [l₀, zero_smul, zero_add] at z
+      rw [l₀, zero_smul, zero_add] at z 
       exact linear_independent_iff.mp i _ z
     -- Finally we put those facts together to show the linear combination is trivial.
     ext (_ | a)
     · simp only [l₀, Finsupp.coe_zero, Pi.zero_apply]
     · erw [Finsupp.congr_fun l₁ a]
       simp only [Finsupp.coe_zero, Pi.zero_apply]
-  dsimp [LinearIndependent.Maximal] at m
+  dsimp [LinearIndependent.Maximal] at m 
   specialize m (range v') i' r
   exact r'' m
 #align union_support_maximal_linear_independent_eq_range_basis union_support_maximal_linearIndependent_eq_range_basis
@@ -693,9 +693,9 @@ theorem Basis.le_span {J : Set M} (v : Basis ι R M) (hJ : span R J = ⊤) : (#r
       rcases mem_range.1 hb with ⟨i, hi⟩
       have : span R J ≤ comap v.repr.to_linear_map (Finsupp.supported R R (⋃ j, S j)) :=
         span_le.2 fun j hj x hx => ⟨_, ⟨⟨j, hj⟩, rfl⟩, hx⟩
-      rw [hJ] at this
+      rw [hJ] at this 
       replace : v.repr (v i) ∈ Finsupp.supported R R (⋃ j, S j) := this trivial
-      rw [v.repr_self, Finsupp.mem_supported, Finsupp.support_single_ne_zero _ one_ne_zero] at this
+      rw [v.repr_self, Finsupp.mem_supported, Finsupp.support_single_ne_zero _ one_ne_zero] at this 
       · subst b
         rcases mem_Union.1 (this (Finset.mem_singleton_self _)) with ⟨j, hj⟩
         exact mem_Union.2 ⟨j, (mem_image _ _ _).2 ⟨i, hj, rfl⟩⟩
@@ -733,9 +733,9 @@ theorem linearIndependent_le_span_aux' {ι : Type _} [Fintype ι] (v : ι → M)
   · apply Finsupp.total
     exact fun i => Span.repr R w ⟨v i, s (mem_range_self i)⟩
   · intro f g h
-    apply_fun Finsupp.total w M R coe  at h
-    simp only [Finsupp.total_total, Submodule.coe_mk, Span.finsupp_total_repr] at h
-    rw [← sub_eq_zero, ← LinearMap.map_sub] at h
+    apply_fun Finsupp.total w M R coe  at h 
+    simp only [Finsupp.total_total, Submodule.coe_mk, Span.finsupp_total_repr] at h 
+    rw [← sub_eq_zero, ← LinearMap.map_sub] at h 
     exact sub_eq_zero.mp (linear_independent_iff.mp i _ h)
 #align linear_independent_le_span_aux' linearIndependent_le_span_aux'
 
@@ -796,7 +796,7 @@ theorem linearIndependent_le_infinite_basis {ι : Type _} (b : Basis ι R M) [In
     (v : κ → M) (i : LinearIndependent R v) : (#κ) ≤ (#ι) :=
   by
   by_contra
-  rw [not_le, ← Cardinal.mk_finset_of_infinite ι] at h
+  rw [not_le, ← Cardinal.mk_finset_of_infinite ι] at h 
   let Φ := fun k : κ => (b.repr (v k)).support
   obtain ⟨s, w : Infinite ↥(Φ ⁻¹' {s})⟩ := Cardinal.exists_infinite_fiber Φ h (by infer_instance)
   let v' := fun k : Φ ⁻¹' {s} => v k
@@ -929,7 +929,7 @@ theorem Basis.mk_eq_rank'.{m} (v : Basis ι R M) :
 theorem Basis.nonempty_fintype_index_of_rank_lt_aleph0 {ι : Type _} (b : Basis ι R M)
     (h : Module.rank R M < ℵ₀) : Nonempty (Fintype ι) := by
   rwa [← Cardinal.lift_lt, ← b.mk_eq_rank, Cardinal.lift_aleph0, Cardinal.lift_lt_aleph0,
-    Cardinal.lt_aleph0_iff_fintype] at h
+    Cardinal.lt_aleph0_iff_fintype] at h 
 #align basis.nonempty_fintype_index_of_rank_lt_aleph_0 Basis.nonempty_fintype_index_of_rank_lt_aleph0
 
 #print Basis.fintypeIndexOfRankLtAleph0 /-
@@ -986,10 +986,10 @@ theorem Ideal.rank_eq {R S : Type _} [CommRing R] [StrongRankCondition R] [Ring
   have : LinearIndependent R fun i => b i • a :=
     by
     have hb := b.linear_independent
-    rw [Fintype.linearIndependent_iff] at hb⊢
+    rw [Fintype.linearIndependent_iff] at hb ⊢
     intro g hg
     apply hb g
-    simp only [← smul_assoc, ← Finset.sum_smul, smul_eq_zero] at hg
+    simp only [← smul_assoc, ← Finset.sum_smul, smul_eq_zero] at hg 
     exact hg.resolve_right ha
   exact
     le_antisymm
@@ -1160,8 +1160,8 @@ def finDimVectorspaceEquiv (n : ℕ) (hn : Module.rank K V = n) : V ≃ₗ[K] Fi
   haveI := nontrivial_of_invariantBasisNumber K
   have : Cardinal.lift.{u} (n : Cardinal.{v}) = Cardinal.lift.{v} (n : Cardinal.{u}) := by simp
   have hn := Cardinal.lift_inj.{v, u}.2 hn
-  rw [this] at hn
-  rw [← @rank_fin_fun K _ _ n] at hn
+  rw [this] at hn 
+  rw [← @rank_fin_fun K _ _ n] at hn 
   haveI : Module.Free K (Fin n → K) := Module.Free.pi _ _
   exact Classical.choice (nonempty_linearEquiv_of_lift_rank_eq hn)
 #align fin_dim_vectorspace_equiv finDimVectorspaceEquiv
@@ -1262,7 +1262,7 @@ theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd
     rintro ⟨d, e⟩
     have h := eq₂ d (-e)
     simp only [add_eq_zero_iff_eq_neg, LinearMap.prod_apply, mem_ker, SetLike.mem_coe,
-      Prod.mk.inj_iff, coprod_apply, map_neg, neg_apply, LinearMap.mem_range, Pi.prod] at h⊢
+      Prod.mk.inj_iff, coprod_apply, map_neg, neg_apply, LinearMap.mem_range, Pi.prod] at h ⊢
     intro hde
     rcases h hde with ⟨c, h₁, h₂⟩
     refine' ⟨c, h₁, _⟩
@@ -1324,7 +1324,7 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} :
   constructor
   · intro h
     let t := Basis.ofVectorSpace K V
-    rw [← t.mk_eq_rank'', Cardinal.le_mk_iff_exists_subset] at h
+    rw [← t.mk_eq_rank'', Cardinal.le_mk_iff_exists_subset] at h 
     rcases h with ⟨s, hst, hsc⟩
     exact ⟨s, hsc, (of_vector_space_index.linear_independent K V).mono hst⟩
   · rintro ⟨s, rfl, si⟩
@@ -1352,7 +1352,7 @@ theorem rank_le_one_iff : Module.rank K V ≤ 1 ↔ ∃ v₀ : V, ∀ v, ∃ r :
   let b := Basis.ofVectorSpace K V
   constructor
   · intro hd
-    rw [← b.mk_eq_rank'', Cardinal.le_one_iff_subsingleton, subsingleton_coe] at hd
+    rw [← b.mk_eq_rank'', Cardinal.le_one_iff_subsingleton, subsingleton_coe] at hd 
     rcases eq_empty_or_nonempty (of_vector_space_index K V) with (hb | ⟨⟨v₀, hv₀⟩⟩)
     · use 0
       have h' : ∀ v : V, v = 0 := by simpa [hb, Submodule.eq_bot_iff] using b.span_eq.symm
@@ -1362,7 +1362,7 @@ theorem rank_le_one_iff : Module.rank K V ≤ 1 ↔ ∃ v₀ : V, ∀ v, ∃ r :
       have h' : (K ∙ v₀) = ⊤ := by simpa [hd.eq_singleton_of_mem hv₀] using b.span_eq
       intro v
       have hv : v ∈ (⊤ : Submodule K V) := mem_top
-      rwa [← h', mem_span_singleton] at hv
+      rwa [← h', mem_span_singleton] at hv 
   · rintro ⟨v₀, hv₀⟩
     have h : (K ∙ v₀) = ⊤ := by ext; simp [mem_span_singleton, hv₀]
     rw [← rank_top, ← h]
@@ -1384,7 +1384,7 @@ theorem rank_submodule_le_one_iff (s : Submodule K V) :
     intro v hv
     obtain ⟨r, hr⟩ := h ⟨v, hv⟩
     use r
-    simp_rw [Subtype.ext_iff, coe_smul, Submodule.coe_mk] at hr
+    simp_rw [Subtype.ext_iff, coe_smul, Submodule.coe_mk] at hr 
     exact hr
   · rintro ⟨v₀, hv₀, h⟩
     use ⟨v₀, hv₀⟩
@@ -1413,8 +1413,8 @@ theorem rank_submodule_le_one_iff' (s : Submodule K V) : Module.rank K s ≤ 1 
         rintro rfl
         simpa using hw0
       rwa [span_singleton_smul_eq (IsUnit.mk0 _ h0) _]
-    · push_neg  at hw
-      rw [← Submodule.eq_bot_iff] at hw
+    · push_neg  at hw 
+      rw [← Submodule.eq_bot_iff] at hw 
       simp [hw]
 #align rank_submodule_le_one_iff' rank_submodule_le_one_iff'
 

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

@@ -87,7 +87,7 @@ variable {K : Type u} {V V₁ V₂ V₃ : Type v} {V' V'₁ : Type v'} {V'' : Ty
 
 variable {ι : Type w} {ι' : Type w'} {η : Type u₁'} {φ : η → Type _}
 
-open Classical BigOperators Cardinal
+open scoped Classical BigOperators Cardinal
 
 open Basis Submodule Function Set
 
@@ -932,11 +932,13 @@ theorem Basis.nonempty_fintype_index_of_rank_lt_aleph0 {ι : Type _} (b : Basis
     Cardinal.lt_aleph0_iff_fintype] at h
 #align basis.nonempty_fintype_index_of_rank_lt_aleph_0 Basis.nonempty_fintype_index_of_rank_lt_aleph0
 
+#print Basis.fintypeIndexOfRankLtAleph0 /-
 /-- If a module has a finite dimension, all bases are indexed by a finite type. -/
 noncomputable def Basis.fintypeIndexOfRankLtAleph0 {ι : Type _} (b : Basis ι R M)
     (h : Module.rank R M < ℵ₀) : Fintype ι :=
   Classical.choice (b.nonempty_fintype_index_of_rank_lt_aleph0 h)
 #align basis.fintype_index_of_rank_lt_aleph_0 Basis.fintypeIndexOfRankLtAleph0
+-/
 
 /-- If a module has a finite dimension, all bases are indexed by a finite set. -/
 theorem Basis.finite_index_of_rank_lt_aleph0 {ι : Type _} {s : Set ι} (b : Basis s R M)
@@ -1178,11 +1180,13 @@ variable [AddCommGroup V₁] [Module K V₁]
 
 variable {K V}
 
+#print Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0 /-
 /-- If a vector space has a finite dimension, the index set of `basis.of_vector_space` is finite. -/
 theorem Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0 (h : Module.rank K V < ℵ₀) :
     (Basis.ofVectorSpaceIndex K V).Finite :=
   finite_def.2 <| (Basis.ofVectorSpace K V).nonempty_fintype_index_of_rank_lt_aleph0 h
 #align basis.finite_of_vector_space_index_of_rank_lt_aleph_0 Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0
+-/
 
 #print rank_span_le /-
 -- TODO how far can we generalise this?
@@ -1196,6 +1200,7 @@ theorem rank_span_le (s : Set V) : Module.rank K (span K s) ≤ (#s) :=
 #align rank_span_le rank_span_le
 -/
 
+#print rank_span_of_finset /-
 theorem rank_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V)) < ℵ₀ :=
   calc
     Module.rank K (span K (↑s : Set V)) ≤ (#(↑s : Set V)) := rank_span_le ↑s
@@ -1203,6 +1208,7 @@ theorem rank_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V
     _ < ℵ₀ := Cardinal.nat_lt_aleph0 _
     
 #align rank_span_of_finset rank_span_of_finset
+-/
 
 theorem rank_quotient_add_rank (p : Submodule K V) :
     Module.rank K (V ⧸ p) + Module.rank K p = Module.rank K V := by

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

@@ -132,12 +132,6 @@ variable {M' : Type v'} [AddCommGroup M'] [Module R M']
 
 variable {M₁ : Type v} [AddCommGroup M₁] [Module R M₁]
 
-/- warning: linear_map.lift_rank_le_of_injective -> LinearMap.lift_rank_le_of_injective is a dubious translation:
-lean 3 declaration is
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 theorem LinearMap.lift_rank_le_of_injective (f : M →ₗ[R] M') (i : Injective f) :
     Cardinal.lift.{v'} (Module.rank R M) ≤ Cardinal.lift.{v} (Module.rank R M') :=
   by
@@ -150,23 +144,11 @@ theorem LinearMap.lift_rank_le_of_injective (f : M →ₗ[R] M') (i : Injective
   exact (li.map' _ <| linear_map.ker_eq_bot.mpr i).image
 #align linear_map.lift_rank_le_of_injective LinearMap.lift_rank_le_of_injective
 
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 theorem LinearMap.rank_le_of_injective (f : M →ₗ[R] M₁) (i : Injective f) :
     Module.rank R M ≤ Module.rank R M₁ :=
   Cardinal.lift_le.1 (f.lift_rank_le_of_injective i)
 #align linear_map.rank_le_of_injective LinearMap.rank_le_of_injective
 
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 theorem rank_le {n : ℕ}
     (H : ∀ s : Finset M, (LinearIndependent R fun i : s => (i : M)) → s.card ≤ n) :
     Module.rank R M ≤ n := by
@@ -215,12 +197,6 @@ theorem rank_map_le (f : M →ₗ[R] M₁) (p : Submodule R M) :
 #align rank_map_le rank_map_le
 -/
 
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 theorem rank_le_of_submodule (s t : Submodule R M) (h : s ≤ t) :
     Module.rank R s ≤ Module.rank R t :=
   (ofLe h).rank_le_of_injective fun ⟨x, hx⟩ ⟨y, hy⟩ eq =>
@@ -246,9 +222,6 @@ theorem LinearEquiv.rank_eq (f : M ≃ₗ[R] M₁) : Module.rank R M = Module.ra
 #align linear_equiv.rank_eq LinearEquiv.rank_eq
 -/
 
-/- warning: rank_eq_of_injective -> rank_eq_of_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align rank_eq_of_injective rank_eq_of_injectiveₓ'. -/
 theorem rank_eq_of_injective (f : M →ₗ[R] M₁) (h : Injective f) :
     Module.rank R M = Module.rank R f.range :=
   (LinearEquiv.ofInjective f h).rank_eq
@@ -264,12 +237,6 @@ theorem LinearEquiv.rank_map_eq (f : M ≃ₗ[R] M₁) (p : Submodule R M) :
 
 variable (R M)
 
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 @[simp]
 theorem rank_top : Module.rank R (⊤ : Submodule R M) = Module.rank R M :=
   by
@@ -279,9 +246,6 @@ theorem rank_top : Module.rank R (⊤ : Submodule R M) = Module.rank R M :=
 
 variable {R M}
 
-/- warning: rank_range_of_surjective -> rank_range_of_surjective is a dubious translation:
-<too large>
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 theorem rank_range_of_surjective (f : M →ₗ[R] M') (h : Surjective f) :
     Module.rank R f.range = Module.rank R M' := by rw [LinearMap.range_eq_top.2 h, rank_top]
 #align rank_range_of_surjective rank_range_of_surjective
@@ -294,12 +258,6 @@ theorem rank_submodule_le (s : Submodule R M) : Module.rank R s ≤ Module.rank
 #align rank_submodule_le rank_submodule_le
 -/
 
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 theorem LinearMap.rank_le_of_surjective (f : M →ₗ[R] M₁) (h : Surjective f) :
     Module.rank R M₁ ≤ Module.rank R M :=
   by
@@ -315,12 +273,6 @@ theorem rank_quotient_le (p : Submodule R M) : Module.rank R (M ⧸ p) ≤ Modul
 
 variable [Nontrivial R]
 
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 theorem cardinal_lift_le_rank_of_linearIndependent.{m} {ι : Type w} {v : ι → M}
     (hv : LinearIndependent R v) :
     Cardinal.lift.{max v m} (#ι) ≤ Cardinal.lift.{max w m} (Module.rank R M) :=
@@ -357,12 +309,6 @@ theorem cardinal_le_rank_of_linearIndependent' {s : Set M}
 
 variable (R M)
 
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 @[simp]
 theorem rank_punit : Module.rank R PUnit = 0 :=
   by
@@ -378,12 +324,6 @@ theorem rank_punit : Module.rank R PUnit = 0 :=
   simpa using LinearIndependent.ne_zero (⟨a, ha⟩ : s) li
 #align rank_punit rank_punit
 
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 @[simp]
 theorem rank_bot : Module.rank R (⊥ : Submodule R M) = 0 :=
   by
@@ -393,12 +333,6 @@ theorem rank_bot : Module.rank R (⊥ : Submodule R M) = 0 :=
 
 variable {R M}
 
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 theorem exists_mem_ne_zero_of_rank_pos {s : Submodule R M} (h : 0 < Module.rank R s) :
     ∃ b : M, b ∈ s ∧ b ≠ 0 :=
   exists_mem_ne_zero_of_ne_bot fun eq => by rw [Eq, rank_bot] at h <;> exact lt_irrefl _ h
@@ -427,12 +361,6 @@ theorem LinearIndependent.set_finite_of_isNoetherian [IsNoetherian R M] {s : Set
 #align linear_independent.set_finite_of_is_noetherian LinearIndependent.set_finite_of_isNoetherian
 -/
 
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 -- One might hope that a finite spanning set implies that any linearly independent set is finite.
 -- While this is true over a division ring
 -- (simply because any linearly independent set can be extended to a basis),
@@ -469,9 +397,6 @@ def basisFintypeOfFiniteSpans (w : Set M) [Fintype w] (s : span R w = ⊤) {ι :
   exact nm
 #align basis_fintype_of_finite_spans basisFintypeOfFiniteSpans
 
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-<too large>
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 -- From [Les familles libres maximales d'un module ont-elles le meme cardinal?][lazarus1973]
 /-- Over any ring `R`, if `b` is a basis for a module `M`,
 and `s` is a maximal linearly independent set,
@@ -573,12 +498,6 @@ theorem infinite_basis_le_maximal_linearIndependent {ι : Type w} (b : Basis ι
 #align infinite_basis_le_maximal_linear_independent infinite_basis_le_maximal_linearIndependent
 -/
 
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-Case conversion may be inaccurate. Consider using '#align complete_lattice.independent.subtype_ne_bot_le_rank CompleteLattice.Independent.subtype_ne_bot_le_rankₓ'. -/
 theorem CompleteLattice.Independent.subtype_ne_bot_le_rank [NoZeroSMulDivisors R M]
     {V : ι → Submodule R M} (hV : CompleteLattice.Independent V) :
     Cardinal.lift.{v} (#{ i : ι // V i ≠ ⊥ }) ≤ Cardinal.lift.{w} (Module.rank R M) :=
@@ -623,12 +542,6 @@ theorem rank_subsingleton [Subsingleton R] : Module.rank R M = 1 :=
 
 variable [NoZeroSMulDivisors R M]
 
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 theorem rank_pos [Nontrivial M] : 0 < Module.rank R M :=
   by
   obtain ⟨x, hx⟩ := exists_ne (0 : M)
@@ -641,12 +554,6 @@ theorem rank_pos [Nontrivial M] : 0 < Module.rank R M :=
 
 variable [Nontrivial R]
 
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-Case conversion may be inaccurate. Consider using '#align rank_zero_iff_forall_zero rank_zero_iff_forall_zeroₓ'. -/
 theorem rank_zero_iff_forall_zero : Module.rank R M = 0 ↔ ∀ x : M, x = 0 :=
   by
   refine' ⟨fun h => _, fun h => _⟩
@@ -658,35 +565,17 @@ theorem rank_zero_iff_forall_zero : Module.rank R M = 0 ↔ ∀ x : M, x = 0 :=
     rw [← rank_top, this, rank_bot]
 #align rank_zero_iff_forall_zero rank_zero_iff_forall_zero
 
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 /-- See `rank_subsingleton` for the reason that `nontrivial R` is needed. -/
 theorem rank_zero_iff : Module.rank R M = 0 ↔ Subsingleton M :=
   rank_zero_iff_forall_zero.trans (subsingleton_iff_forall_eq 0).symm
 #align rank_zero_iff rank_zero_iff
 
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 theorem rank_pos_iff_exists_ne_zero : 0 < Module.rank R M ↔ ∃ x : M, x ≠ 0 :=
   by
   rw [← not_iff_not]
   simpa using rank_zero_iff_forall_zero
 #align rank_pos_iff_exists_ne_zero rank_pos_iff_exists_ne_zero
 
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 theorem rank_pos_iff_nontrivial : 0 < Module.rank R M ↔ Nontrivial M :=
   rank_pos_iff_exists_ne_zero.trans (nontrivial_iff_exists_ne 0).symm
 #align rank_pos_iff_nontrivial rank_pos_iff_nontrivial
@@ -730,12 +619,6 @@ theorem mk_eq_mk_of_basis (v : Basis ι R M) (v' : Basis ι' R M) :
 #align mk_eq_mk_of_basis mk_eq_mk_of_basis
 -/
 
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 /-- Given two bases indexed by `ι` and `ι'` of an `R`-module, where `R` satisfies the invariant
 basis number property, an equiv `ι ≃ ι' `. -/
 def Basis.indexEquiv (v : Basis ι R M) (v' : Basis ι' R M) : ι ≃ ι' :=
@@ -756,12 +639,6 @@ variable {R : Type u} [Ring R] [RankCondition R]
 
 variable {M : Type v} [AddCommGroup M] [Module R M]
 
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 /-- An auxiliary lemma for `basis.le_span`.
 
 If `R` satisfies the rank condition,
@@ -782,12 +659,6 @@ theorem Basis.le_span'' {ι : Type _} [Fintype ι] (b : Basis ι R M) {w : Set M
     simpa using s
 #align basis.le_span'' Basis.le_span''
 
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 /--
 Another auxiliary lemma for `basis.le_span`, which does not require assuming the basis is finite,
 but still assumes we have a finite spanning set.
@@ -802,12 +673,6 @@ theorem basis_le_span' {ι : Type _} (b : Basis ι R M) {w : Set M} [Fintype w]
   exact Basis.le_span'' b s
 #align basis_le_span' basis_le_span'
 
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 -- Note that if `R` satisfies the strong rank condition,
 -- this also follows from `linear_independent_le_span` below.
 /-- If `R` satisfies the rank condition,
@@ -854,12 +719,6 @@ variable {M : Type v} [AddCommGroup M] [Module R M]
 
 open Submodule
 
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 -- An auxiliary lemma for `linear_independent_le_span'`,
 -- with the additional assumption that the linearly independent family is finite.
 theorem linearIndependent_le_span_aux' {ι : Type _} [Fintype ι] (v : ι → M)
@@ -897,12 +756,6 @@ def linearIndependentFintypeOfLeSpanFintype {ι : Type _} (v : ι → M) (i : Li
 #align linear_independent_fintype_of_le_span_fintype linearIndependentFintypeOfLeSpanFintype
 -/
 
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 /-- If `R` satisfies the strong rank condition,
 then for any linearly independent family `v : ι → M`
 contained in the span of some finite `w : set M`,
@@ -917,12 +770,6 @@ theorem linearIndependent_le_span' {ι : Type _} (v : ι → M) (i : LinearIndep
   exact linearIndependent_le_span_aux' v i w s
 #align linear_independent_le_span' linearIndependent_le_span'
 
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 /-- If `R` satisfies the strong rank condition,
 then for any linearly independent family `v : ι → M`
 and any finite spanning set `w : set M`,
@@ -936,24 +783,12 @@ theorem linearIndependent_le_span {ι : Type _} (v : ι → M) (i : LinearIndepe
   exact le_top
 #align linear_independent_le_span linearIndependent_le_span
 
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 /-- A version of `linear_independent_le_span` for `finset`. -/
 theorem linearIndependent_le_span_finset {ι : Type _} (v : ι → M) (i : LinearIndependent R v)
     (w : Finset M) (s : span R (w : Set M) = ⊤) : (#ι) ≤ w.card := by
   simpa only [Finset.coe_sort_coe, Fintype.card_coe] using linearIndependent_le_span v i w s
 #align linear_independent_le_span_finset linearIndependent_le_span_finset
 
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 /-- An auxiliary lemma for `linear_independent_le_basis`:
 we handle the case where the basis `b` is infinite.
 -/
@@ -975,12 +810,6 @@ theorem linearIndependent_le_infinite_basis {ι : Type _} (b : Basis ι R M) [In
   exact w.false
 #align linear_independent_le_infinite_basis linearIndependent_le_infinite_basis
 
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 /-- Over any ring `R` satisfying the strong rank condition,
 if `b` is a basis for a module `M`,
 and `s` is a linearly independent set,
@@ -1009,12 +838,6 @@ theorem Basis.card_le_card_of_linearIndependent_aux {R : Type _} [Ring R] [Stron
 #align basis.card_le_card_of_linear_independent_aux Basis.card_le_card_of_linearIndependent_aux
 -/
 
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 -- When the basis is not infinite this need not be true!
 /-- Over any ring `R` satisfying the strong rank condition,
 if `b` is an infinite basis for a module `M`,
@@ -1055,12 +878,6 @@ theorem Basis.mk_range_eq_rank (v : Basis ι R M) : (#range v) = Module.rank R M
 #align basis.mk_range_eq_rank Basis.mk_range_eq_rank
 -/
 
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 /-- If a vector space has a finite basis, then its dimension (seen as a cardinal) is equal to the
 cardinality of the basis. -/
 theorem rank_eq_card_basis {ι : Type w} [Fintype ι] (h : Basis ι R M) :
@@ -1070,12 +887,6 @@ theorem rank_eq_card_basis {ι : Type w} [Fintype ι] (h : Basis ι R M) :
   rw [← h.mk_range_eq_rank, Cardinal.mk_fintype, Set.card_range_of_injective h.injective]
 #align rank_eq_card_basis rank_eq_card_basis
 
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 theorem Basis.card_le_card_of_linearIndependent {ι : Type _} [Fintype ι] (b : Basis ι R M)
     {ι' : Type _} [Fintype ι'] {v : ι' → M} (hv : LinearIndependent R v) :
     Fintype.card ι' ≤ Fintype.card ι :=
@@ -1092,9 +903,6 @@ theorem Basis.card_le_card_of_submodule (N : Submodule R M) [Fintype ι] (b : Ba
 #align basis.card_le_card_of_submodule Basis.card_le_card_of_submodule
 -/
 
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 theorem Basis.card_le_card_of_le {N O : Submodule R M} (hNO : N ≤ O) [Fintype ι] (b : Basis ι R O)
     [Fintype ι'] (b' : Basis ι' R N) : Fintype.card ι' ≤ Fintype.card ι :=
   b.card_le_card_of_linearIndependent
@@ -1117,12 +925,6 @@ theorem Basis.mk_eq_rank'.{m} (v : Basis ι R M) :
 #align basis.mk_eq_rank' Basis.mk_eq_rank'
 -/
 
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 /-- If a module has a finite dimension, all bases are indexed by a finite type. -/
 theorem Basis.nonempty_fintype_index_of_rank_lt_aleph0 {ι : Type _} (b : Basis ι R M)
     (h : Module.rank R M < ℵ₀) : Nonempty (Fintype ι) := by
@@ -1130,24 +932,12 @@ theorem Basis.nonempty_fintype_index_of_rank_lt_aleph0 {ι : Type _} (b : Basis
     Cardinal.lt_aleph0_iff_fintype] at h
 #align basis.nonempty_fintype_index_of_rank_lt_aleph_0 Basis.nonempty_fintype_index_of_rank_lt_aleph0
 
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 /-- If a module has a finite dimension, all bases are indexed by a finite type. -/
 noncomputable def Basis.fintypeIndexOfRankLtAleph0 {ι : Type _} (b : Basis ι R M)
     (h : Module.rank R M < ℵ₀) : Fintype ι :=
   Classical.choice (b.nonempty_fintype_index_of_rank_lt_aleph0 h)
 #align basis.fintype_index_of_rank_lt_aleph_0 Basis.fintypeIndexOfRankLtAleph0
 
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 /-- If a module has a finite dimension, all bases are indexed by a finite set. -/
 theorem Basis.finite_index_of_rank_lt_aleph0 {ι : Type _} {s : Set ι} (b : Basis s R M)
     (h : Module.rank R M < ℵ₀) : s.Finite :=
@@ -1171,9 +961,6 @@ theorem rank_span_set {s : Set M} (hs : LinearIndependent R (fun x => x : s →
 #align rank_span_set rank_span_set
 -/
 
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 /-- If `N` is a submodule in a free, finitely generated module,
 do induction on adjoining a linear independent element to a submodule. -/
 def Submodule.inductionOnRank [IsDomain R] [Fintype ι] (b : Basis ι R M)
@@ -1186,9 +973,6 @@ def Submodule.inductionOnRank [IsDomain R] [Fintype ι] (b : Basis ι R M)
     simpa using b.card_le_card_of_linear_independent hli
 #align submodule.induction_on_rank Submodule.inductionOnRank
 
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 /-- If `S` a finite-dimensional ring extension of `R` which is free as an `R`-module,
 then the rank of an ideal `I` of `S` over `R` is the same as the rank of `S`.
 -/
@@ -1314,12 +1098,6 @@ theorem LinearEquiv.nonempty_equiv_iff_rank_eq :
 #align linear_equiv.nonempty_equiv_iff_rank_eq LinearEquiv.nonempty_equiv_iff_rank_eq
 -/
 
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 /-- The rank of `M × N` is `(module.rank R M).lift + (module.rank R N).lift`. -/
 @[simp]
 theorem rank_prod :
@@ -1330,12 +1108,6 @@ theorem rank_prod :
     lift_umax'] using ((choose_basis K V).Prod (choose_basis K V')).mk_eq_rank.symm
 #align rank_prod rank_prod
 
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 /-- If `M` and `N` lie in the same universe, the rank of `M × N` is
   `(module.rank R M) + (module.rank R N)`. -/
 theorem rank_prod' : Module.rank K (V × V₁) = Module.rank K V + Module.rank K V₁ := by simp
@@ -1347,12 +1119,6 @@ variable [∀ i, AddCommGroup (φ i)] [∀ i, Module K (φ i)] [∀ i, Module.Fr
 
 open LinearMap
 
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 /-- The rank of a finite product is the sum of the ranks. -/
 @[simp]
 theorem rank_pi [Finite η] : Module.rank K (∀ i, φ i) = Cardinal.sum fun i => Module.rank K (φ i) :=
@@ -1365,56 +1131,26 @@ theorem rank_pi [Finite η] : Module.rank K (∀ i, φ i) = Cardinal.sum fun i =
 
 variable [Fintype η]
 
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 theorem rank_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] [Module.Free K V] :
     Module.rank K (η → V) = Fintype.card η * Module.rank K V := by
   rw [rank_pi, Cardinal.sum_const', Cardinal.mk_fintype]
 #align rank_fun rank_fun
 
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 theorem rank_fun_eq_lift_mul :
     Module.rank K (η → V) =
       (Fintype.card η : Cardinal.{max u₁' v}) * Cardinal.lift.{u₁'} (Module.rank K V) :=
   by rw [rank_pi, Cardinal.sum_const, Cardinal.mk_fintype, Cardinal.lift_natCast]
 #align rank_fun_eq_lift_mul rank_fun_eq_lift_mul
 
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 theorem rank_fun' : Module.rank K (η → K) = Fintype.card η := by
   rw [rank_fun_eq_lift_mul, rank_self, Cardinal.lift_one, mul_one, Cardinal.natCast_inj]
 #align rank_fun' rank_fun'
 
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 theorem rank_fin_fun (n : ℕ) : Module.rank K (Fin n → K) = n := by simp [rank_fun']
 #align rank_fin_fun rank_fin_fun
 
 end Fintype
 
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 -- TODO: merge with the `finrank` content
 /-- An `n`-dimensional `K`-vector space is equivalent to `fin n → K`. -/
 def finDimVectorspaceEquiv (n : ℕ) (hn : Module.rank K V = n) : V ≃ₗ[K] Fin n → K :=
@@ -1442,12 +1178,6 @@ variable [AddCommGroup V₁] [Module K V₁]
 
 variable {K V}
 
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 /-- If a vector space has a finite dimension, the index set of `basis.of_vector_space` is finite. -/
 theorem Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0 (h : Module.rank K V < ℵ₀) :
     (Basis.ofVectorSpaceIndex K V).Finite :=
@@ -1466,12 +1196,6 @@ theorem rank_span_le (s : Set V) : Module.rank K (span K s) ≤ (#s) :=
 #align rank_span_le rank_span_le
 -/
 
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 theorem rank_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V)) < ℵ₀ :=
   calc
     Module.rank K (span K (↑s : Set V)) ≤ (#(↑s : Set V)) := rank_span_le ↑s
@@ -1480,12 +1204,6 @@ theorem rank_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V
     
 #align rank_span_of_finset rank_span_of_finset
 
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 theorem rank_quotient_add_rank (p : Submodule K V) :
     Module.rank K (V ⧸ p) + Module.rank K p = Module.rank K V := by
   classical exact
@@ -1493,9 +1211,6 @@ theorem rank_quotient_add_rank (p : Submodule K V) :
       rank_prod'.symm.trans f.rank_eq
 #align rank_quotient_add_rank rank_quotient_add_rank
 
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 /-- rank-nullity theorem -/
 theorem rank_range_add_rank_ker (f : V →ₗ[K] V₁) :
     Module.rank K f.range + Module.rank K f.ker = Module.rank K V :=
@@ -1504,9 +1219,6 @@ theorem rank_range_add_rank_ker (f : V →ₗ[K] V₁) :
   rw [← f.quot_ker_equiv_range.rank_eq, rank_quotient_add_rank]
 #align rank_range_add_rank_ker rank_range_add_rank_ker
 
-/- warning: rank_eq_of_surjective -> rank_eq_of_surjective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align rank_eq_of_surjective rank_eq_of_surjectiveₓ'. -/
 theorem rank_eq_of_surjective (f : V →ₗ[K] V₁) (h : Surjective f) :
     Module.rank K V = Module.rank K V₁ + Module.rank K f.ker := by
   rw [← rank_range_add_rank_ker f, ← rank_range_of_surjective f h]
@@ -1520,9 +1232,6 @@ variable [AddCommGroup V₃] [Module K V₃]
 
 open LinearMap
 
-/- warning: rank_add_rank_split -> rank_add_rank_split is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align rank_add_rank_split rank_add_rank_splitₓ'. -/
 /-- This is mostly an auxiliary lemma for `submodule.rank_sup_add_rank_inf_eq`. -/
 theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd : V₁ →ₗ[K] V₂)
     (ce : V₁ →ₗ[K] V₃) (hde : ⊤ ≤ db.range ⊔ eb.range) (hgd : ker cd = ⊥)
@@ -1554,9 +1263,6 @@ theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd
     rw [h₂, _root_.neg_neg]
 #align rank_add_rank_split rank_add_rank_split
 
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-<too large>
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 theorem Submodule.rank_sup_add_rank_inf_eq (s t : Submodule K V) :
     Module.rank K (s ⊔ t : Submodule K V) + Module.rank K (s ⊓ t : Submodule K V) =
       Module.rank K s + Module.rank K t :=
@@ -1573,9 +1279,6 @@ theorem Submodule.rank_sup_add_rank_inf_eq (s t : Submodule K V) :
       exact ⟨⟨b₁, hb₁, hb₂⟩, rfl, rfl⟩)
 #align submodule.rank_sup_add_rank_inf_eq Submodule.rank_sup_add_rank_inf_eq
 
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-<too large>
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 theorem Submodule.rank_add_le_rank_add_rank (s t : Submodule K V) :
     Module.rank K (s ⊔ t : Submodule K V) ≤ Module.rank K s + Module.rank K t := by
   rw [← Submodule.rank_sup_add_rank_inf_eq]; exact self_le_add_right _ _
@@ -1602,12 +1305,6 @@ def Basis.ofRankEqZero {ι : Type _} [IsEmpty ι] (hV : Module.rank K V = 0) : B
 #align basis.of_rank_eq_zero Basis.ofRankEqZero
 -/
 
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 @[simp]
 theorem Basis.ofRankEqZero_apply {ι : Type _} [IsEmpty ι] (hV : Module.rank K V = 0) (i : ι) :
     Basis.ofRankEqZero hV i = 0 :=
@@ -1629,12 +1326,6 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} :
 #align le_rank_iff_exists_linear_independent le_rank_iff_exists_linearIndependent
 -/
 
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 theorem le_rank_iff_exists_linearIndependent_finset {n : ℕ} :
     ↑n ≤ Module.rank K V ↔
       ∃ s : Finset V, s.card = n ∧ LinearIndependent K (coe : (s : Set V) → V) :=
@@ -1674,12 +1365,6 @@ theorem rank_le_one_iff : Module.rank K V ≤ 1 ↔ ∃ v₀ : V, ∀ v, ∃ r :
 #align rank_le_one_iff rank_le_one_iff
 -/
 
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 /-- A submodule has dimension at most `1` if and only if there is a
 single vector in the submodule such that the submodule is contained in
 its span. -/
@@ -1704,12 +1389,6 @@ theorem rank_submodule_le_one_iff (s : Submodule K V) :
     exact hr
 #align rank_submodule_le_one_iff rank_submodule_le_one_iff
 
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 /-- A submodule has dimension at most `1` if and only if there is a
 single vector, not necessarily in the submodule, such that the
 submodule is contained in its span. -/
@@ -1749,12 +1428,6 @@ theorem Submodule.rank_le_one_iff_isPrincipal (W : Submodule K V) :
 #align submodule.rank_le_one_iff_is_principal Submodule.rank_le_one_iff_isPrincipal
 -/
 
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 theorem Module.rank_le_one_iff_top_isPrincipal :
     Module.rank K V ≤ 1 ↔ (⊤ : Submodule K V).IsPrincipal := by
   rw [← Submodule.rank_le_one_iff_isPrincipal, rank_top]
@@ -1794,12 +1467,6 @@ theorem rank_le_domain (f : V →ₗ[K] V₁) : rank f ≤ Module.rank K V :=
 #align linear_map.rank_le_domain LinearMap.rank_le_domain
 -/
 
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-Case conversion may be inaccurate. Consider using '#align linear_map.rank_zero LinearMap.rank_zeroₓ'. -/
 @[simp]
 theorem rank_zero [Nontrivial K] : rank (0 : V →ₗ[K] V') = 0 := by
   rw [rank, LinearMap.range_zero, rank_bot]
@@ -1823,9 +1490,6 @@ theorem lift_rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
 #align linear_map.lift_rank_comp_le_right LinearMap.lift_rank_comp_le_right
 -/
 
-/- warning: linear_map.lift_rank_comp_le -> LinearMap.lift_rank_comp_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.lift_rank_comp_le LinearMap.lift_rank_comp_leₓ'. -/
 /-- The rank of the composition of two maps is less than the minimum of their ranks. -/
 theorem lift_rank_comp_le (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
     Cardinal.lift.{v'} (rank (f.comp g)) ≤
@@ -1841,9 +1505,6 @@ theorem rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) : rank
 #align linear_map.rank_comp_le_right LinearMap.rank_comp_le_right
 -/
 
-/- warning: linear_map.rank_comp_le -> LinearMap.rank_comp_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.rank_comp_le LinearMap.rank_comp_leₓ'. -/
 /-- The rank of the composition of two maps is less than the minimum of their ranks.
 
 See `lift_rank_comp_le` for the universe-polymorphic version. -/
@@ -1860,9 +1521,6 @@ variable [DivisionRing K] [AddCommGroup V] [Module K V] [AddCommGroup V₁] [Mod
 
 variable [AddCommGroup V'] [Module K V']
 
-/- warning: linear_map.rank_add_le -> LinearMap.rank_add_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.rank_add_le LinearMap.rank_add_leₓ'. -/
 theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
   calc
     rank (f + g) ≤ Module.rank K (f.range ⊔ g.range : Submodule K V') :=
@@ -1877,18 +1535,12 @@ theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
     
 #align linear_map.rank_add_le LinearMap.rank_add_le
 
-/- warning: linear_map.rank_finset_sum_le -> LinearMap.rank_finset_sum_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.rank_finset_sum_le LinearMap.rank_finset_sum_leₓ'. -/
 theorem rank_finset_sum_le {η} (s : Finset η) (f : η → V →ₗ[K] V') :
     rank (∑ d in s, f d) ≤ ∑ d in s, rank (f d) :=
   @Finset.sum_hom_rel _ _ _ _ _ (fun a b => rank a ≤ b) f (fun d => rank (f d)) s
     (le_of_eq rank_zero) fun i g c h => le_trans (rank_add_le _ _) (add_le_add_left h _)
 #align linear_map.rank_finset_sum_le LinearMap.rank_finset_sum_le
 
-/- warning: linear_map.le_rank_iff_exists_linear_independent -> LinearMap.le_rank_iff_exists_linearIndependent is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.le_rank_iff_exists_linear_independent LinearMap.le_rank_iff_exists_linearIndependentₓ'. -/
 theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'} :
     c ≤ rank f ↔
       ∃ s : Set V,
@@ -1911,9 +1563,6 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'}
     exact inj_on_iff_injective.2 this.injective
 #align linear_map.le_rank_iff_exists_linear_independent LinearMap.le_rank_iff_exists_linearIndependent
 
-/- warning: linear_map.le_rank_iff_exists_linear_independent_finset -> LinearMap.le_rank_iff_exists_linearIndependent_finset is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.le_rank_iff_exists_linear_independent_finset LinearMap.le_rank_iff_exists_linearIndependent_finsetₓ'. -/
 theorem le_rank_iff_exists_linearIndependent_finset {n : ℕ} {f : V →ₗ[K] V'} :
     ↑n ≤ rank f ↔ ∃ s : Finset V, s.card = n ∧ LinearIndependent K fun x : (s : Set V) => f x :=
   by

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

@@ -463,9 +463,7 @@ def basisFintypeOfFiniteSpans (w : Set M) [Fintype w] (s : span R w = ⊤) {ι :
   -- Now there is some `x : ι` not in `S`, since `ι` is infinite.
   obtain ⟨x, nm⟩ := Infinite.exists_not_mem_finset S
   -- However it must be in the span of the finite subset,
-  have k' : b x ∈ span R bS := by
-    rw [k]
-    exact mem_top
+  have k' : b x ∈ span R bS := by rw [k]; exact mem_top
   -- giving the desire contradiction.
   refine' b.linear_independent.not_mem_span_image _ k'
   exact nm
@@ -501,20 +499,15 @@ theorem union_support_maximal_linearIndependent_eq_range_basis {ι : Type w} (b
     simpa [w] using congr_arg (fun m => (b.repr m) b') p
   have r'' : range v ≠ range v' := by
     intro e
-    have p : b b' ∈ range v' := by
-      use none
-      rfl
+    have p : b b' ∈ range v' := by use none; rfl
     rw [← e] at p
     exact r' p
   have inj' : injective v' := by
     rintro (_ | k) (_ | k) z
     · rfl
-    · exfalso
-      exact r' ⟨k, z.symm⟩
-    · exfalso
-      exact r' ⟨k, z⟩
-    · congr
-      exact i.injective z
+    · exfalso; exact r' ⟨k, z.symm⟩
+    · exfalso; exact r' ⟨k, z⟩
+    · congr ; exact i.injective z
   -- The key step in the proof is checking that this strictly larger family is linearly independent.
   have i' : LinearIndependent R (coe : range v' → M) :=
     by
@@ -661,9 +654,7 @@ theorem rank_zero_iff_forall_zero : Module.rank R M = 0 ↔ ∀ x : M, x = 0 :=
     obtain ⟨x, hx⟩ := h
     letI : Nontrivial M := nontrivial_of_ne _ _ hx
     exact rank_pos.ne'
-  · have : (⊤ : Submodule R M) = ⊥ := by
-      ext x
-      simp [h x]
+  · have : (⊤ : Submodule R M) = ⊥ := by ext x; simp [h x]
     rw [← rank_top, this, rank_bot]
 #align rank_zero_iff_forall_zero rank_zero_iff_forall_zero
 
@@ -1050,11 +1041,7 @@ theorem Basis.mk_eq_rank'' {ι : Type v} (v : Basis ι R M) : (#ι) = Module.ran
   · trans
     swap
     apply le_ciSup (Cardinal.bddAbove_range.{v, v} _)
-    exact
-      ⟨Set.range v, by
-        convert v.reindex_range.linear_independent
-        ext
-        simp⟩
+    exact ⟨Set.range v, by convert v.reindex_range.linear_independent; ext; simp⟩
     exact (Cardinal.mk_range_eq v v.injective).ge
   · apply ciSup_le'
     rintro ⟨s, li⟩
@@ -1179,9 +1166,7 @@ theorem rank_span {v : ι → M} (hv : LinearIndependent R v) :
 
 #print rank_span_set /-
 theorem rank_span_set {s : Set M} (hs : LinearIndependent R (fun x => x : s → M)) :
-    Module.rank R ↥(span R s) = (#s) :=
-  by
-  rw [← @set_of_mem_eq _ s, ← Subtype.range_coe_subtype]
+    Module.rank R ↥(span R s) = (#s) := by rw [← @set_of_mem_eq _ s, ← Subtype.range_coe_subtype];
   exact rank_span hs
 #align rank_span_set rank_span_set
 -/
@@ -1592,10 +1577,8 @@ theorem Submodule.rank_sup_add_rank_inf_eq (s t : Submodule K V) :
 <too large>
 Case conversion may be inaccurate. Consider using '#align submodule.rank_add_le_rank_add_rank Submodule.rank_add_le_rank_add_rankₓ'. -/
 theorem Submodule.rank_add_le_rank_add_rank (s t : Submodule K V) :
-    Module.rank K (s ⊔ t : Submodule K V) ≤ Module.rank K s + Module.rank K t :=
-  by
-  rw [← Submodule.rank_sup_add_rank_inf_eq]
-  exact self_le_add_right _ _
+    Module.rank K (s ⊔ t : Submodule K V) ≤ Module.rank K s + Module.rank K t := by
+  rw [← Submodule.rank_sup_add_rank_inf_eq]; exact self_le_add_right _ _
 #align submodule.rank_add_le_rank_add_rank Submodule.rank_add_le_rank_add_rank
 
 end
@@ -1684,9 +1667,7 @@ theorem rank_le_one_iff : Module.rank K V ≤ 1 ↔ ∃ v₀ : V, ∀ v, ∃ r :
       have hv : v ∈ (⊤ : Submodule K V) := mem_top
       rwa [← h', mem_span_singleton] at hv
   · rintro ⟨v₀, hv₀⟩
-    have h : (K ∙ v₀) = ⊤ := by
-      ext
-      simp [mem_span_singleton, hv₀]
+    have h : (K ∙ v₀) = ⊤ := by ext; simp [mem_span_singleton, hv₀]
     rw [← rank_top, ← h]
     refine' (rank_span_le _).trans_eq _
     simp
@@ -1918,9 +1899,7 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'}
   refine' ⟨fun h => _, _⟩
   · rcases le_rank_iff_exists_linearIndependent.1 h with ⟨s, rfl, si⟩
     refine' ⟨g '' s, Cardinal.mk_image_eq_lift _ _ fg.injective, _⟩
-    replace fg : ∀ x, f (g x) = x
-    · intro x
-      convert congr_arg Subtype.val (fg x)
+    replace fg : ∀ x, f (g x) = x; · intro x; convert congr_arg Subtype.val (fg x)
     replace si : LinearIndependent K fun x : s => f (g x)
     · simpa only [fg] using si.map' _ (ker_subtype _)
     exact si.image_of_comp s g f

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

@@ -247,10 +247,7 @@ theorem LinearEquiv.rank_eq (f : M ≃ₗ[R] M₁) : Module.rank R M = Module.ra
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align rank_eq_of_injective rank_eq_of_injectiveₓ'. -/
 theorem rank_eq_of_injective (f : M →ₗ[R] M₁) (h : Injective f) :
     Module.rank R M = Module.rank R f.range :=
@@ -283,10 +280,7 @@ theorem rank_top : Module.rank R (⊤ : Submodule R M) = Module.rank R M :=
 variable {R M}
 
 /- warning: rank_range_of_surjective -> rank_range_of_surjective is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align rank_range_of_surjective rank_range_of_surjectiveₓ'. -/
 theorem rank_range_of_surjective (f : M →ₗ[R] M') (h : Surjective f) :
     Module.rank R f.range = Module.rank R M' := by rw [LinearMap.range_eq_top.2 h, rank_top]
@@ -478,10 +472,7 @@ def basisFintypeOfFiniteSpans (w : Set M) [Fintype w] (s : span R w = ⊤) {ι :
 #align basis_fintype_of_finite_spans basisFintypeOfFiniteSpans
 
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(RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b) (v k))))) (Set.univ.{u3} ι))
+<too large>
 Case conversion may be inaccurate. Consider using '#align union_support_maximal_linear_independent_eq_range_basis union_support_maximal_linearIndependent_eq_range_basisₓ'. -/
 -- From [Les familles libres maximales d'un module ont-elles le meme cardinal?][lazarus1973]
 /-- Over any ring `R`, if `b` is a basis for a module `M`,
@@ -1115,10 +1106,7 @@ theorem Basis.card_le_card_of_submodule (N : Submodule R M) [Fintype ι] (b : Ba
 -/
 
 /- warning: basis.card_le_card_of_le -> Basis.card_le_card_of_le is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.card_le_card_of_le Basis.card_le_card_of_leₓ'. -/
 theorem Basis.card_le_card_of_le {N O : Submodule R M} (hNO : N ≤ O) [Fintype ι] (b : Basis ι R O)
     [Fintype ι'] (b' : Basis ι' R N) : Fintype.card ι' ≤ Fintype.card ι :=
@@ -1199,10 +1187,7 @@ theorem rank_span_set {s : Set M} (hs : LinearIndependent R (fun x => x : s →
 -/
 
 /- warning: submodule.induction_on_rank -> Submodule.inductionOnRank is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.induction_on_rank Submodule.inductionOnRankₓ'. -/
 /-- If `N` is a submodule in a free, finitely generated module,
 do induction on adjoining a linear independent element to a submodule. -/
@@ -1217,10 +1202,7 @@ def Submodule.inductionOnRank [IsDomain R] [Fintype ι] (b : Basis ι R M)
 #align submodule.induction_on_rank Submodule.inductionOnRank
 
 /- warning: ideal.rank_eq -> Ideal.rank_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.rank_eq Ideal.rank_eqₓ'. -/
 /-- If `S` a finite-dimensional ring extension of `R` which is free as an `R`-module,
 then the rank of an ideal `I` of `S` over `R` is the same as the rank of `S`.
@@ -1527,10 +1509,7 @@ theorem rank_quotient_add_rank (p : Submodule K V) :
 #align rank_quotient_add_rank rank_quotient_add_rank
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align rank_range_add_rank_ker rank_range_add_rank_kerₓ'. -/
 /-- rank-nullity theorem -/
 theorem rank_range_add_rank_ker (f : V →ₗ[K] V₁) :
@@ -1541,10 +1520,7 @@ theorem rank_range_add_rank_ker (f : V →ₗ[K] V₁) :
 #align rank_range_add_rank_ker rank_range_add_rank_ker
 
 /- warning: rank_eq_of_surjective -> rank_eq_of_surjective is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align rank_eq_of_surjective rank_eq_of_surjectiveₓ'. -/
 theorem rank_eq_of_surjective (f : V →ₗ[K] V₁) (h : Surjective f) :
     Module.rank K V = Module.rank K V₁ + Module.rank K f.ker := by
@@ -1560,10 +1536,7 @@ variable [AddCommGroup V₃] [Module K V₃]
 open LinearMap
 
 /- warning: rank_add_rank_split -> rank_add_rank_split is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} {V₂ : Type.{u2}} {V₃ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] [_inst_8 : AddCommGroup.{u2} V₂] [_inst_9 : Module.{u1, u2} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8)] [_inst_10 : AddCommGroup.{u2} V₃] [_inst_11 : Module.{u1, u2} K V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10)] (db : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (eb : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (cd : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (ce : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11), (LE.le.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Top.top.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _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 _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 _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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) db) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) eb))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (LinearMap.ker.{u1, u1, u2, u2, u2} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K 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(DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_3) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) db cd) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) eb ce)) -> (forall (d : V₂) (e : V₃), (Eq.{succ u2} V (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) => V₂ -> V) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) db d) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) => V₃ -> V) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) eb e)) -> (Exists.{succ u2} V₁ (fun (c : V₁) => And (Eq.{succ u2} V₂ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₁ V₂ (Ring.toSemiring.{u1} K 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+<too large>
 Case conversion may be inaccurate. Consider using '#align rank_add_rank_split rank_add_rank_splitₓ'. -/
 /-- This is mostly an auxiliary lemma for `submodule.rank_sup_add_rank_inf_eq`. -/
 theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd : V₁ →ₗ[K] V₂)
@@ -1597,10 +1570,7 @@ theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd
 #align rank_add_rank_split rank_add_rank_split
 
 /- warning: submodule.rank_sup_add_rank_inf_eq -> Submodule.rank_sup_add_rank_inf_eq is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align submodule.rank_sup_add_rank_inf_eq Submodule.rank_sup_add_rank_inf_eqₓ'. -/
 theorem Submodule.rank_sup_add_rank_inf_eq (s t : Submodule K V) :
     Module.rank K (s ⊔ t : Submodule K V) + Module.rank K (s ⊓ t : Submodule K V) =
@@ -1619,10 +1589,7 @@ theorem Submodule.rank_sup_add_rank_inf_eq (s t : Submodule K V) :
 #align submodule.rank_sup_add_rank_inf_eq Submodule.rank_sup_add_rank_inf_eq
 
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 Case conversion may be inaccurate. Consider using '#align submodule.rank_add_le_rank_add_rank Submodule.rank_add_le_rank_add_rankₓ'. -/
 theorem Submodule.rank_add_le_rank_add_rank (s t : Submodule K V) :
     Module.rank K (s ⊔ t : Submodule K V) ≤ Module.rank K s + Module.rank K t :=
@@ -1876,10 +1843,7 @@ theorem lift_rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
 -/
 
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 /-- The rank of the composition of two maps is less than the minimum of their ranks. -/
 theorem lift_rank_comp_le (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
@@ -1897,10 +1861,7 @@ theorem rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) : rank
 -/
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.rank_comp_le LinearMap.rank_comp_leₓ'. -/
 /-- The rank of the composition of two maps is less than the minimum of their ranks.
 
@@ -1919,10 +1880,7 @@ variable [DivisionRing K] [AddCommGroup V] [Module K V] [AddCommGroup V₁] [Mod
 variable [AddCommGroup V'] [Module K V']
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.rank_add_le LinearMap.rank_add_leₓ'. -/
 theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
   calc
@@ -1939,10 +1897,7 @@ theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
 #align linear_map.rank_add_le LinearMap.rank_add_le
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.rank_finset_sum_le LinearMap.rank_finset_sum_leₓ'. -/
 theorem rank_finset_sum_le {η} (s : Finset η) (f : η → V →ₗ[K] V') :
     rank (∑ d in s, f d) ≤ ∑ d in s, rank (f d) :=
@@ -1951,10 +1906,7 @@ theorem rank_finset_sum_le {η} (s : Finset η) (f : η → V →ₗ[K] V') :
 #align linear_map.rank_finset_sum_le LinearMap.rank_finset_sum_le
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.le_rank_iff_exists_linear_independent LinearMap.le_rank_iff_exists_linearIndependentₓ'. -/
 theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'} :
     c ≤ rank f ↔
@@ -1981,10 +1933,7 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'}
 #align linear_map.le_rank_iff_exists_linear_independent LinearMap.le_rank_iff_exists_linearIndependent
 
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(Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)) V (coeSubtype.{succ u2} V (fun (x : V) => Membership.Mem.{u2, u2} V (Set.{u2} V) (Set.hasMem.{u2} V) x ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)))))) x)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
-but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {n : Nat} {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} (Nat.cast.{succ u3} Cardinal.{u3} Cardinal.instNatCastCardinal.{u3} n) (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Finset.{u2} V) (fun (s : Finset.{u2} V) => And (Eq.{1} Nat (Finset.card.{u2} V s) n) (LinearIndependent.{u2, u1, u3} (Set.Elem.{u2} V (Finset.toSet.{u2} V s)) K V' (fun (x : Set.Elem.{u2} V (Finset.toSet.{u2} V s)) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => V') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x (Finset.toSet.{u2} V s)) x)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.le_rank_iff_exists_linear_independent_finset LinearMap.le_rank_iff_exists_linearIndependent_finsetₓ'. -/
 theorem le_rank_iff_exists_linearIndependent_finset {n : ℕ} {f : V →ₗ[K] V'} :
     ↑n ≤ rank f ↔ ∃ s : Finset V, s.card = n ∧ LinearIndependent K fun x : (s : Set V) => f x :=

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

@@ -136,7 +136,7 @@ variable {M₁ : Type v} [AddCommGroup M₁] [Module R M₁]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Injective.{succ u2, succ u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ (max u2 u3)} Cardinal.{max u2 u3} Cardinal.hasLe.{max u2 u3} (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Cardinal.lift.{u2, u3} (Module.rank.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Injective.{succ u2, succ u3} M M' (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{max (succ u2) (succ u3)} Cardinal.{max u2 u3} Cardinal.instLECardinal.{max u2 u3} (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Cardinal.lift.{u2, u3} (Module.rank.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Injective.{succ u2, succ u3} M M' (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{max (succ u2) (succ u3)} Cardinal.{max u2 u3} Cardinal.instLECardinal.{max u2 u3} (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Cardinal.lift.{u2, u3} (Module.rank.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)))
 Case conversion may be inaccurate. Consider using '#align linear_map.lift_rank_le_of_injective LinearMap.lift_rank_le_of_injectiveₓ'. -/
 theorem LinearMap.lift_rank_le_of_injective (f : M →ₗ[R] M') (i : Injective f) :
     Cardinal.lift.{v'} (Module.rank R M) ≤ Cardinal.lift.{v} (Module.rank R M') :=
@@ -154,7 +154,7 @@ theorem LinearMap.lift_rank_le_of_injective (f : M →ₗ[R] M') (i : Injective
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Injective.{succ u2, succ u2} M M₁ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) => M -> M₁) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.rank.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Injective.{succ u2, succ u2} M M₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.rank.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Injective.{succ u2, succ u2} M M₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.rank.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7))
 Case conversion may be inaccurate. Consider using '#align linear_map.rank_le_of_injective LinearMap.rank_le_of_injectiveₓ'. -/
 theorem LinearMap.rank_le_of_injective (f : M →ₗ[R] M₁) (i : Injective f) :
     Module.rank R M ≤ Module.rank R M₁ :=
@@ -250,7 +250,7 @@ theorem LinearEquiv.rank_eq (f : M ≃ₗ[R] M₁) : Module.rank R M = Module.ra
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Injective.{succ u2, succ u2} M M₁ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) => M -> M₁) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.rank.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) M₁ (Submodule.setLike.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7)) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Injective.{succ u2, succ u2} M M₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.rank.{u1, u2} R (Subtype.{succ u2} M₁ (fun (x : M₁) => Membership.mem.{u2, u2} M₁ (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) M₁ (Submodule.setLike.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7)) x (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Injective.{succ u2, succ u2} M M₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.rank.{u1, u2} R (Subtype.{succ u2} M₁ (fun (x : M₁) => Membership.mem.{u2, u2} M₁ (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) M₁ (Submodule.setLike.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7)) x (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))))
 Case conversion may be inaccurate. Consider using '#align rank_eq_of_injective rank_eq_of_injectiveₓ'. -/
 theorem rank_eq_of_injective (f : M →ₗ[R] M₁) (h : Injective f) :
     Module.rank R M = Module.rank R f.range :=
@@ -286,7 +286,7 @@ variable {R M}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{succ u2, succ u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Eq.{succ (succ u3)} Cardinal.{u3} (Module.rank.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Module.rank.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{succ u2, succ u3} M M' (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Eq.{succ (succ u3)} Cardinal.{u3} (Module.rank.{u1, u3} R (Subtype.{succ u3} M' (fun (x : M') => Membership.mem.{u3, u3} M' (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) x (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Module.rank.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{succ u2, succ u3} M M' (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Eq.{succ (succ u3)} Cardinal.{u3} (Module.rank.{u1, u3} R (Subtype.{succ u3} M' (fun (x : M') => Membership.mem.{u3, u3} M' (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) x (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Module.rank.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5))
 Case conversion may be inaccurate. Consider using '#align rank_range_of_surjective rank_range_of_surjectiveₓ'. -/
 theorem rank_range_of_surjective (f : M →ₗ[R] M') (h : Surjective f) :
     Module.rank R f.range = Module.rank R M' := by rw [LinearMap.range_eq_top.2 h, rank_top]
@@ -304,7 +304,7 @@ theorem rank_submodule_le (s : Submodule R M) : Module.rank R s ≤ Module.rank
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} M M₁ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) => M -> M₁) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Module.rank.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} M M₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} M M₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))
 Case conversion may be inaccurate. Consider using '#align linear_map.rank_le_of_surjective LinearMap.rank_le_of_surjectiveₓ'. -/
 theorem LinearMap.rank_le_of_surjective (f : M →ₗ[R] M₁) (h : Surjective f) :
     Module.rank R M₁ ≤ Module.rank R M :=
@@ -481,7 +481,7 @@ def basisFintypeOfFiniteSpans (w : Set M) [Fintype w] (s : span R w = ⊤) {ι :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_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_8 : Nontrivial.{u1} R] {ι : Type.{u3}} (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {κ : Type.{u4}} (v : κ -> M) (i : LinearIndependent.{u4, u1, u2} κ R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), (LinearIndependent.Maximal.{u1, u2, u4} κ R (Ring.toSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 v i) -> (Eq.{succ u3} (Set.{u3} ι) (Set.iUnion.{u3, succ u4} ι κ (fun (k : κ) => (fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Finset.{u3} ι) (Set.{u3} ι) (HasLiftT.mk.{succ u3, succ u3} (Finset.{u3} ι) (Set.{u3} ι) (CoeTCₓ.coe.{succ u3, succ u3} (Finset.{u3} ι) (Set.{u3} ι) (Finset.Set.hasCoeT.{u3} ι))) (Finsupp.support.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => M -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Basis.repr.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b) (v k))))) (Set.univ.{u3} ι))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_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_8 : Nontrivial.{u1} R] {ι : Type.{u3}} (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {κ : Type.{u4}} (v : κ -> M) (i : LinearIndependent.{u4, u1, u2} κ R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), (LinearIndependent.Maximal.{u1, u2, u4} κ R (Ring.toSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 v i) -> (Eq.{succ u3} (Set.{u3} ι) (Set.iUnion.{u3, succ u4} ι κ (fun (k : κ) => Finset.toSet.{u3} ι (Finsupp.support.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b) (v k))))) (Set.univ.{u3} ι))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_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_8 : Nontrivial.{u1} R] {ι : Type.{u3}} (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {κ : Type.{u4}} (v : κ -> M) (i : LinearIndependent.{u4, u1, u2} κ R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), (LinearIndependent.Maximal.{u1, u2, u4} κ R (Ring.toSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 v i) -> (Eq.{succ u3} (Set.{u3} ι) (Set.iUnion.{u3, succ u4} ι κ (fun (k : κ) => Finset.toSet.{u3} ι (Finsupp.support.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b) (v k))))) (Set.univ.{u3} ι))
 Case conversion may be inaccurate. Consider using '#align union_support_maximal_linear_independent_eq_range_basis union_support_maximal_linearIndependent_eq_range_basisₓ'. -/
 -- From [Les familles libres maximales d'un module ont-elles le meme cardinal?][lazarus1973]
 /-- Over any ring `R`, if `b` is a basis for a module `M`,
@@ -1544,7 +1544,7 @@ theorem rank_range_add_rank_ker (f : V →ₗ[K] V₁) :
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} V V₁ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) => V -> V₁) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Module.rank.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} V V₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => V₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Module.rank.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f))) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)))))
+  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} V V₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => V₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Module.rank.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f))) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)))))
 Case conversion may be inaccurate. Consider using '#align rank_eq_of_surjective rank_eq_of_surjectiveₓ'. -/
 theorem rank_eq_of_surjective (f : V →ₗ[K] V₁) (h : Surjective f) :
     Module.rank K V = Module.rank K V₁ + Module.rank K f.ker := by
@@ -1563,7 +1563,7 @@ open LinearMap
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} {V₂ : Type.{u2}} {V₃ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] [_inst_8 : AddCommGroup.{u2} V₂] [_inst_9 : Module.{u1, u2} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8)] [_inst_10 : AddCommGroup.{u2} V₃] [_inst_11 : Module.{u1, u2} K V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10)] (db : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (eb : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (cd : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (ce : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11), (LE.le.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Top.top.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _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 _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 _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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) db) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) eb))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (LinearMap.ker.{u1, u1, u2, u2, u2} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) cd) (Bot.bot.{u2} (Submodule.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Submodule.hasBot.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7))) -> (Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_3) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) db cd) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) eb ce)) -> (forall (d : V₂) (e : V₃), (Eq.{succ u2} V (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) => V₂ -> V) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) db d) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) => V₃ -> V) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) eb e)) -> (Exists.{succ u2} V₁ (fun (c : V₁) => And (Eq.{succ u2} V₂ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) cd c) d) (Eq.{succ u2} V₃ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11) => V₁ -> V₃) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₁ V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) ce c) e)))) -> (Eq.{succ (succ u2)} Cardinal.{u2} (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.rank.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7)) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_9) (Module.rank.{u1, u2} K V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_11)))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} {V₂ : Type.{u2}} {V₃ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] [_inst_8 : AddCommGroup.{u2} V₂] [_inst_9 : Module.{u1, u2} K V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8)] [_inst_10 : AddCommGroup.{u2} V₃] [_inst_11 : Module.{u1, u2} K V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10)] (db : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (eb : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (cd : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (ce : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11), (LE.le.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (Top.top.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Sup.sup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) db) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) eb))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (LinearMap.ker.{u1, u1, u2, u2, u2} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) cd) (Bot.bot.{u2} (Submodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Submodule.instBotSubmodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7))) -> (Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_3) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHomCompTriple.ids.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) db cd) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHomCompTriple.ids.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) eb ce)) -> (forall (d : V₂) (e : V₃), (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₂) => V) d) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) V₂ (fun (_x : V₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₂) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) db d) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) V₃ (fun (_x : V₃) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₃) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) eb e)) -> (Exists.{succ u2} V₁ (fun (c : V₁) => And (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₁) => V₂) c) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) cd c) d) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₁) => V₃) c) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₁) => V₃) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₁ V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) ce c) e)))) -> (Eq.{succ (succ u2)} Cardinal.{u2} (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.rank.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7)) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_9) (Module.rank.{u1, u2} K V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_11)))
+  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} {V₂ : Type.{u2}} {V₃ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] [_inst_8 : AddCommGroup.{u2} V₂] [_inst_9 : Module.{u1, u2} K V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8)] [_inst_10 : AddCommGroup.{u2} V₃] [_inst_11 : Module.{u1, u2} K V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10)] (db : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (eb : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (cd : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (ce : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11), (LE.le.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) 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K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) db) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) eb))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (LinearMap.ker.{u1, u1, u2, u2, u2} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) cd) (Bot.bot.{u2} (Submodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Submodule.instBotSubmodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7))) -> (Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_3) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHomCompTriple.ids.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) db cd) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHomCompTriple.ids.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) eb ce)) -> (forall (d : V₂) (e : V₃), (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V₂) => V) d) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) V₂ (fun (_x : V₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V₂) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) db d) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) V₃ (fun (_x : V₃) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V₃) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) eb e)) -> (Exists.{succ u2} V₁ (fun (c : V₁) => And (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V₁) => V₂) c) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) cd c) d) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V₁) => V₃) c) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V₁) => V₃) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₁ V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) ce c) e)))) -> (Eq.{succ (succ u2)} Cardinal.{u2} (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.rank.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7)) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_9) (Module.rank.{u1, u2} K V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_11)))
 Case conversion may be inaccurate. Consider using '#align rank_add_rank_split rank_add_rank_splitₓ'. -/
 /-- This is mostly an auxiliary lemma for `submodule.rank_sup_add_rank_inf_eq`. -/
 theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd : V₁ →ₗ[K] V₂)
@@ -1954,7 +1954,7 @@ theorem rank_finset_sum_le {η} (s : Finset η) (f : η → V →ₗ[K] V') :
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {c : Cardinal.{u3}} {f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.hasLe.{u3} c (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Set.{u2} V) (fun (s : Set.{u2} V) => And (Eq.{succ (succ (max u2 u3))} Cardinal.{max u2 u3} (Cardinal.lift.{u3, u2} (Cardinal.mk.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s))) (Cardinal.lift.{u2, u3} c)) (LinearIndependent.{u2, u1, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s) K V' (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s) => coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) => V -> V') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} K K V V' (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s) V (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s) V (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s) V (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s) V (coeSubtype.{succ u2} V (fun (x : V) => Membership.Mem.{u2, u2} V (Set.{u2} V) (Set.hasMem.{u2} V) x s))))) x)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {c : Cardinal.{u3}} {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} c (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Set.{u2} V) (fun (s : Set.{u2} V) => And (Eq.{max (succ (succ u2)) (succ (succ u3))} Cardinal.{max u2 u3} (Cardinal.lift.{u3, u2} (Cardinal.mk.{u2} (Set.Elem.{u2} V s))) (Cardinal.lift.{u2, u3} c)) (LinearIndependent.{u2, u1, u3} (Set.Elem.{u2} V s) K V' (fun (x : Set.Elem.{u2} V s) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => V') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s) x)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
+  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {c : Cardinal.{u3}} {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} c (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Set.{u2} V) (fun (s : Set.{u2} V) => And (Eq.{max (succ (succ u2)) (succ (succ u3))} Cardinal.{max u2 u3} (Cardinal.lift.{u3, u2} (Cardinal.mk.{u2} (Set.Elem.{u2} V s))) (Cardinal.lift.{u2, u3} c)) (LinearIndependent.{u2, u1, u3} (Set.Elem.{u2} V s) K V' (fun (x : Set.Elem.{u2} V s) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => V') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s) x)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
 Case conversion may be inaccurate. Consider using '#align linear_map.le_rank_iff_exists_linear_independent LinearMap.le_rank_iff_exists_linearIndependentₓ'. -/
 theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'} :
     c ≤ rank f ↔
@@ -1984,7 +1984,7 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'}
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {n : Nat} {f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.hasLe.{u3} ((fun (a : Type) (b : Type.{succ u3}) [self : HasLiftT.{1, succ (succ u3)} a b] => self.0) Nat 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_inst_7) => V -> V') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} K K V V' (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)) V (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) ((fun (a 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(Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)) V (coeSubtype.{succ u2} V (fun (x : V) => Membership.Mem.{u2, u2} V (Set.{u2} V) (Set.hasMem.{u2} V) x ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)))))) x)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {n : Nat} {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} (Nat.cast.{succ u3} Cardinal.{u3} Cardinal.instNatCastCardinal.{u3} n) (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Finset.{u2} V) (fun (s : Finset.{u2} V) => And (Eq.{1} Nat (Finset.card.{u2} V s) n) (LinearIndependent.{u2, u1, u3} (Set.Elem.{u2} V (Finset.toSet.{u2} V s)) K V' (fun (x : Set.Elem.{u2} V (Finset.toSet.{u2} V s)) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => V') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x (Finset.toSet.{u2} V s)) x)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
+  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {n : Nat} {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} (Nat.cast.{succ u3} Cardinal.{u3} Cardinal.instNatCastCardinal.{u3} n) (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Finset.{u2} V) (fun (s : Finset.{u2} V) => And (Eq.{1} Nat (Finset.card.{u2} V s) n) (LinearIndependent.{u2, u1, u3} (Set.Elem.{u2} V (Finset.toSet.{u2} V s)) K V' (fun (x : Set.Elem.{u2} V (Finset.toSet.{u2} V s)) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => V') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x (Finset.toSet.{u2} V s)) x)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
 Case conversion may be inaccurate. Consider using '#align linear_map.le_rank_iff_exists_linear_independent_finset LinearMap.le_rank_iff_exists_linearIndependent_finsetₓ'. -/
 theorem le_rank_iff_exists_linearIndependent_finset {n : ℕ} {f : V →ₗ[K] V'} :
     ↑n ≤ rank f ↔ ∃ s : Finset V, s.card = n ∧ LinearIndependent K fun x : (s : Set V) => f x :=

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

@@ -136,7 +136,7 @@ variable {M₁ : Type v} [AddCommGroup M₁] [Module R M₁]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Injective.{succ u2, succ u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ (max u2 u3)} Cardinal.{max u2 u3} Cardinal.hasLe.{max u2 u3} (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Cardinal.lift.{u2, u3} (Module.rank.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Injective.{succ u2, succ u3} M M' (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{max (succ u2) (succ u3)} Cardinal.{max u2 u3} Cardinal.instLECardinal.{max u2 u3} (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Cardinal.lift.{u2, u3} (Module.rank.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Injective.{succ u2, succ u3} M M' (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{max (succ u2) (succ u3)} Cardinal.{max u2 u3} Cardinal.instLECardinal.{max u2 u3} (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Cardinal.lift.{u2, u3} (Module.rank.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)))
 Case conversion may be inaccurate. Consider using '#align linear_map.lift_rank_le_of_injective LinearMap.lift_rank_le_of_injectiveₓ'. -/
 theorem LinearMap.lift_rank_le_of_injective (f : M →ₗ[R] M') (i : Injective f) :
     Cardinal.lift.{v'} (Module.rank R M) ≤ Cardinal.lift.{v} (Module.rank R M') :=
@@ -154,7 +154,7 @@ theorem LinearMap.lift_rank_le_of_injective (f : M →ₗ[R] M') (i : Injective
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Injective.{succ u2, succ u2} M M₁ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) => M -> M₁) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.rank.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Injective.{succ u2, succ u2} M M₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.rank.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Injective.{succ u2, succ u2} M M₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.rank.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7))
 Case conversion may be inaccurate. Consider using '#align linear_map.rank_le_of_injective LinearMap.rank_le_of_injectiveₓ'. -/
 theorem LinearMap.rank_le_of_injective (f : M →ₗ[R] M₁) (i : Injective f) :
     Module.rank R M ≤ Module.rank R M₁ :=
@@ -176,12 +176,7 @@ theorem rank_le {n : ℕ}
   exact linearIndependent_bounded_of_finset_linearIndependent_bounded H _ li
 #align rank_le rank_le
 
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-Case conversion may be inaccurate. Consider using '#align lift_rank_range_le lift_rank_range_leₓ'. -/
+#print lift_rank_range_le /-
 theorem lift_rank_range_le (f : M →ₗ[R] M') :
     Cardinal.lift.{v} (Module.rank R f.range) ≤ Cardinal.lift.{v'} (Module.rank R M) :=
   by
@@ -197,39 +192,28 @@ theorem lift_rank_range_le (f : M →ₗ[R] M') :
     convert li.comp (Equiv.Set.rangeSplittingImageEquiv f s) (Equiv.injective _) using 1
   · exact (cardinal.lift_mk_eq'.mpr ⟨Equiv.Set.rangeSplittingImageEquiv f s⟩).ge
 #align lift_rank_range_le lift_rank_range_le
+-/
 
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+#print rank_range_le /-
 theorem rank_range_le (f : M →ₗ[R] M₁) : Module.rank R f.range ≤ Module.rank R M := by
   simpa using lift_rank_range_le f
 #align rank_range_le rank_range_le
+-/
 
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+#print lift_rank_map_le /-
 theorem lift_rank_map_le (f : M →ₗ[R] M') (p : Submodule R M) :
     Cardinal.lift.{v} (Module.rank R (p.map f)) ≤ Cardinal.lift.{v'} (Module.rank R p) :=
   by
   have h := lift_rank_range_le (f.comp (Submodule.subtype p))
   rwa [LinearMap.range_comp, range_subtype] at h
 #align lift_rank_map_le lift_rank_map_le
+-/
 
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(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 p)) (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 p) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p))
-Case conversion may be inaccurate. Consider using '#align rank_map_le rank_map_leₓ'. -/
+#print rank_map_le /-
 theorem rank_map_le (f : M →ₗ[R] M₁) (p : Submodule R M) :
     Module.rank R (p.map f) ≤ Module.rank R p := by simpa using lift_rank_map_le f p
 #align rank_map_le rank_map_le
+-/
 
 /- warning: rank_le_of_submodule -> rank_le_of_submodule is a dubious translation:
 lean 3 declaration is
@@ -266,24 +250,20 @@ theorem LinearEquiv.rank_eq (f : M ≃ₗ[R] M₁) : Module.rank R M = Module.ra
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Injective.{succ u2, succ u2} M M₁ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) 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R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))))
 but is expected to have type
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_inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.rank.{u1, u2} R (Subtype.{succ u2} M₁ (fun (x : M₁) => Membership.mem.{u2, u2} M₁ (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) M₁ (Submodule.setLike.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7)) x (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ 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_inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))))
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_inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.rank.{u1, u2} R (Subtype.{succ u2} M₁ (fun (x : M₁) => Membership.mem.{u2, u2} M₁ (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) M₁ 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 Case conversion may be inaccurate. Consider using '#align rank_eq_of_injective rank_eq_of_injectiveₓ'. -/
 theorem rank_eq_of_injective (f : M →ₗ[R] M₁) (h : Injective f) :
     Module.rank R M = Module.rank R f.range :=
   (LinearEquiv.ofInjective f h).rank_eq
 #align rank_eq_of_injective rank_eq_of_injective
 
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(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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 f) p))) (Module.rank.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_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 p)) (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 p) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p))
-Case conversion may be inaccurate. Consider using '#align linear_equiv.rank_map_eq LinearEquiv.rank_map_eqₓ'. -/
+#print LinearEquiv.rank_map_eq /-
 /-- Pushforwards of submodules along a `linear_equiv` have the same dimension. -/
 theorem LinearEquiv.rank_map_eq (f : M ≃ₗ[R] M₁) (p : Submodule R M) :
     Module.rank R (p.map (f : M →ₗ[R] M₁)) = Module.rank R p :=
   (f.submoduleMap p).rank_eq.symm
 #align linear_equiv.rank_map_eq LinearEquiv.rank_map_eq
+-/
 
 variable (R M)
 
@@ -306,7 +286,7 @@ variable {R M}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{succ u2, succ u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Eq.{succ (succ u3)} Cardinal.{u3} (Module.rank.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Module.rank.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{succ u2, succ u3} M M' (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Eq.{succ (succ u3)} Cardinal.{u3} (Module.rank.{u1, u3} R (Subtype.{succ u3} M' (fun (x : M') => Membership.mem.{u3, u3} M' (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) x (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Module.rank.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{succ u2, succ u3} M M' (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Eq.{succ (succ u3)} Cardinal.{u3} (Module.rank.{u1, u3} R (Subtype.{succ u3} M' (fun (x : M') => Membership.mem.{u3, u3} M' (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) x (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Module.rank.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5))
 Case conversion may be inaccurate. Consider using '#align rank_range_of_surjective rank_range_of_surjectiveₓ'. -/
 theorem rank_range_of_surjective (f : M →ₗ[R] M') (h : Surjective f) :
     Module.rank R f.range = Module.rank R M' := by rw [LinearMap.range_eq_top.2 h, rank_top]
@@ -324,7 +304,7 @@ theorem rank_submodule_le (s : Submodule R M) : Module.rank R s ≤ Module.rank
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} M M₁ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) => M -> M₁) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Module.rank.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} M M₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} M M₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))
 Case conversion may be inaccurate. Consider using '#align linear_map.rank_le_of_surjective LinearMap.rank_le_of_surjectiveₓ'. -/
 theorem LinearMap.rank_le_of_surjective (f : M →ₗ[R] M₁) (h : Surjective f) :
     Module.rank R M₁ ≤ Module.rank R M :=
@@ -1550,7 +1530,7 @@ theorem rank_quotient_add_rank (p : Submodule K V) :
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7), Eq.{succ (succ u2)} Cardinal.{u2} (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) V₁ (Submodule.setLike.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7)) (LinearMap.range.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) f)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) f)) (Submodule.module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) f))) (Module.rank.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)))) (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7), Eq.{succ (succ u2)} Cardinal.{u2} 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_inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) f))) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K 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(DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) f)) (Submodule.module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) f))) (Module.rank.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => 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(DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f))) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)))) (Module.rank.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)
+  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7), Eq.{succ (succ u2)} Cardinal.{u2} 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_inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) f))) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K 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(DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) f)) (Submodule.module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K 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(DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)))) (Module.rank.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)
 Case conversion may be inaccurate. Consider using '#align rank_range_add_rank_ker rank_range_add_rank_kerₓ'. -/
 /-- rank-nullity theorem -/
 theorem rank_range_add_rank_ker (f : V →ₗ[K] V₁) :
@@ -1564,7 +1544,7 @@ theorem rank_range_add_rank_ker (f : V →ₗ[K] V₁) :
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} V V₁ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) => V -> V₁) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Module.rank.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} V V₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => V₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Module.rank.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K 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(DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f))) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)))))
+  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} V V₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => V₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Module.rank.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f))) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)))))
 Case conversion may be inaccurate. Consider using '#align rank_eq_of_surjective rank_eq_of_surjectiveₓ'. -/
 theorem rank_eq_of_surjective (f : V →ₗ[K] V₁) (h : Surjective f) :
     Module.rank K V = Module.rank K V₁ + Module.rank K f.ker := by
@@ -1583,7 +1563,7 @@ open LinearMap
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} {V₂ : Type.{u2}} {V₃ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] [_inst_8 : AddCommGroup.{u2} V₂] [_inst_9 : Module.{u1, u2} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8)] [_inst_10 : AddCommGroup.{u2} V₃] [_inst_11 : Module.{u1, u2} K V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10)] (db : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (eb : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (cd : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (ce : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11), (LE.le.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Top.top.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _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 _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 _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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) db) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) eb))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (LinearMap.ker.{u1, u1, u2, u2, u2} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K 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(DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_3) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) db cd) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) eb ce)) -> (forall (d : V₂) (e : V₃), (Eq.{succ u2} V (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) => V₂ -> V) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) db d) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) => V₃ -> V) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) eb e)) -> (Exists.{succ u2} V₁ (fun (c : V₁) => And (Eq.{succ u2} V₂ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) cd c) d) (Eq.{succ u2} V₃ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11) => V₁ -> V₃) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₁ V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) ce c) e)))) -> (Eq.{succ (succ u2)} Cardinal.{u2} (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.rank.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7)) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_9) (Module.rank.{u1, u2} K V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_11)))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} {V₂ : Type.{u2}} {V₃ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] [_inst_8 : AddCommGroup.{u2} V₂] [_inst_9 : Module.{u1, u2} K V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8)] [_inst_10 : AddCommGroup.{u2} V₃] [_inst_11 : Module.{u1, u2} K V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10)] (db : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (eb : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (cd : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (ce : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11), (LE.le.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (Top.top.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Sup.sup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) db) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) eb))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (LinearMap.ker.{u1, u1, u2, u2, u2} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) cd) (Bot.bot.{u2} (Submodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Submodule.instBotSubmodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7))) -> (Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_3) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHomCompTriple.ids.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) db cd) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K 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(DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) V₃ (fun (_x : V₃) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₃) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) eb e)) -> (Exists.{succ u2} V₁ (fun (c : V₁) => And (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₁) => V₂) c) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) cd c) d) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₁) => V₃) c) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₁) => V₃) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₁ V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) ce c) e)))) -> (Eq.{succ (succ u2)} Cardinal.{u2} (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.rank.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7)) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_9) (Module.rank.{u1, u2} K V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_11)))
+  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} {V₂ : Type.{u2}} {V₃ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] [_inst_8 : AddCommGroup.{u2} V₂] [_inst_9 : Module.{u1, u2} K V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8)] [_inst_10 : AddCommGroup.{u2} V₃] [_inst_11 : Module.{u1, u2} K V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10)] (db : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (eb : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (cd : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (ce : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11), (LE.le.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (Top.top.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Sup.sup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} K V 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K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) db) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) eb))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (LinearMap.ker.{u1, u1, u2, u2, u2} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) cd) (Bot.bot.{u2} (Submodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Submodule.instBotSubmodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7))) -> (Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_3) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHomCompTriple.ids.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) db cd) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHomCompTriple.ids.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) eb ce)) -> (forall (d : V₂) (e : V₃), (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₂) => V) d) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) V₂ (fun (_x : V₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₂) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) db d) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) V₃ (fun (_x : V₃) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₃) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) eb e)) -> (Exists.{succ u2} V₁ (fun (c : V₁) => And (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₁) => V₂) c) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) cd c) d) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₁) => V₃) c) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V₁) => V₃) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₁ V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) ce c) e)))) -> (Eq.{succ (succ u2)} Cardinal.{u2} (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.rank.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7)) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_9) (Module.rank.{u1, u2} K V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_11)))
 Case conversion may be inaccurate. Consider using '#align rank_add_rank_split rank_add_rank_splitₓ'. -/
 /-- This is mostly an auxiliary lemma for `submodule.rank_sup_add_rank_inf_eq`. -/
 theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd : V₁ →ₗ[K] V₂)
@@ -1974,7 +1954,7 @@ theorem rank_finset_sum_le {η} (s : Finset η) (f : η → V →ₗ[K] V') :
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {c : Cardinal.{u3}} {f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.hasLe.{u3} c (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Set.{u2} V) (fun (s : Set.{u2} V) => And (Eq.{succ (succ (max u2 u3))} Cardinal.{max u2 u3} (Cardinal.lift.{u3, u2} (Cardinal.mk.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s))) (Cardinal.lift.{u2, u3} c)) (LinearIndependent.{u2, u1, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s) K V' (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s) => coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) => V -> V') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} K K V V' (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s) V (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s) V (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s) V (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s) V (coeSubtype.{succ u2} V (fun (x : V) => Membership.Mem.{u2, u2} V (Set.{u2} V) (Set.hasMem.{u2} V) x s))))) x)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {c : Cardinal.{u3}} {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} c (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Set.{u2} V) (fun (s : Set.{u2} V) => And (Eq.{max (succ (succ u2)) (succ (succ u3))} Cardinal.{max u2 u3} (Cardinal.lift.{u3, u2} (Cardinal.mk.{u2} (Set.Elem.{u2} V s))) (Cardinal.lift.{u2, u3} c)) (LinearIndependent.{u2, u1, u3} (Set.Elem.{u2} V s) K V' (fun (x : Set.Elem.{u2} V s) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => V') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s) x)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
+  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {c : Cardinal.{u3}} {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} c (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Set.{u2} V) (fun (s : Set.{u2} V) => And (Eq.{max (succ (succ u2)) (succ (succ u3))} Cardinal.{max u2 u3} (Cardinal.lift.{u3, u2} (Cardinal.mk.{u2} (Set.Elem.{u2} V s))) (Cardinal.lift.{u2, u3} c)) (LinearIndependent.{u2, u1, u3} (Set.Elem.{u2} V s) K V' (fun (x : Set.Elem.{u2} V s) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => V') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s) x)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
 Case conversion may be inaccurate. Consider using '#align linear_map.le_rank_iff_exists_linear_independent LinearMap.le_rank_iff_exists_linearIndependentₓ'. -/
 theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'} :
     c ≤ rank f ↔
@@ -2004,7 +1984,7 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'}
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {n : Nat} {f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.hasLe.{u3} ((fun (a : Type) (b : Type.{succ u3}) [self : HasLiftT.{1, succ (succ u3)} a b] => self.0) Nat Cardinal.{u3} (HasLiftT.mk.{1, succ (succ u3)} Nat Cardinal.{u3} (CoeTCₓ.coe.{1, succ (succ u3)} Nat Cardinal.{u3} (Nat.castCoe.{succ u3} Cardinal.{u3} Cardinal.hasNatCast.{u3}))) n) (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Finset.{u2} V) (fun (s : Finset.{u2} V) => And (Eq.{1} Nat (Finset.card.{u2} V s) n) (LinearIndependent.{u2, u1, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)) K V' (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)) => coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) => V -> V') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} K K V V' (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)) V (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)) V (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)) V (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)) V (coeSubtype.{succ u2} V (fun (x : V) => Membership.Mem.{u2, u2} V (Set.{u2} V) (Set.hasMem.{u2} V) x ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)))))) x)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {n : Nat} {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} (Nat.cast.{succ u3} Cardinal.{u3} Cardinal.instNatCastCardinal.{u3} n) (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Finset.{u2} V) (fun (s : Finset.{u2} V) => And (Eq.{1} Nat (Finset.card.{u2} V s) n) (LinearIndependent.{u2, u1, u3} (Set.Elem.{u2} V (Finset.toSet.{u2} V s)) K V' (fun (x : Set.Elem.{u2} V (Finset.toSet.{u2} V s)) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => V') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x (Finset.toSet.{u2} V s)) x)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
+  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {n : Nat} {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} (Nat.cast.{succ u3} Cardinal.{u3} Cardinal.instNatCastCardinal.{u3} n) (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Finset.{u2} V) (fun (s : Finset.{u2} V) => And (Eq.{1} Nat (Finset.card.{u2} V s) n) (LinearIndependent.{u2, u1, u3} (Set.Elem.{u2} V (Finset.toSet.{u2} V s)) K V' (fun (x : Set.Elem.{u2} V (Finset.toSet.{u2} V s)) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => V') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x (Finset.toSet.{u2} V s)) x)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
 Case conversion may be inaccurate. Consider using '#align linear_map.le_rank_iff_exists_linear_independent_finset LinearMap.le_rank_iff_exists_linearIndependent_finsetₓ'. -/
 theorem le_rank_iff_exists_linearIndependent_finset {n : ℕ} {f : V →ₗ[K] V'} :
     ↑n ≤ rank f ↔ ∃ s : Finset V, s.card = n ∧ LinearIndependent K fun x : (s : Set V) => f x :=

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

@@ -233,7 +233,7 @@ theorem rank_map_le (f : M →ₗ[R] M₁) (p : Submodule R M) :
 
 /- warning: rank_le_of_submodule -> rank_le_of_submodule is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (s : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (t : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{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)))) s t) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Module.rank.{u1, u2} 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)) s) (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 s) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 s)) (Module.rank.{u1, u2} 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)) t) (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 t) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 t)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (s : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (t : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SetLike.partialOrder.{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)))) s t) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Module.rank.{u1, u2} 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)) s) (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 s) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 s)) (Module.rank.{u1, u2} 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)) t) (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 t) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 t)))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (s : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (t : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))) s t) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_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 s)) (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 s) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 s)) (Module.rank.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_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 t)) (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 t) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 t)))
 Case conversion may be inaccurate. Consider using '#align rank_le_of_submodule rank_le_of_submoduleₓ'. -/
@@ -421,7 +421,7 @@ variable {R M}
 
 /- warning: exists_mem_ne_zero_of_rank_pos -> exists_mem_ne_zero_of_rank_pos is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_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_8 : Nontrivial.{u1} R] {s : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3}, (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} 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)) s) (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 s) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 s))) -> (Exists.{succ u2} M (fun (b : M) => And (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)) b s) (Ne.{succ u2} M b (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)))))))))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_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_8 : Nontrivial.{u1} R] {s : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3}, (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toHasLt.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} 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)) s) (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 s) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 s))) -> (Exists.{succ u2} M (fun (b : M) => And (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)) b s) (Ne.{succ u2} M b (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)))))))))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_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_8 : Nontrivial.{u1} R] {s : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3}, (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (Zero.toOfNat0.{succ u2} Cardinal.{u2} Cardinal.instZeroCardinal.{u2})) (Module.rank.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_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 s)) (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 s) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 s))) -> (Exists.{succ u2} M (fun (b : M) => And (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)) b s) (Ne.{succ u2} M b (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))))))))))
 Case conversion may be inaccurate. Consider using '#align exists_mem_ne_zero_of_rank_pos exists_mem_ne_zero_of_rank_posₓ'. -/
@@ -661,7 +661,7 @@ variable [NoZeroSMulDivisors R M]
 
 /- warning: rank_pos -> rank_pos is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_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))))] [_inst_5 : Nontrivial.{u2} M], LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
+  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))))] [_inst_5 : Nontrivial.{u2} M], LT.lt.{succ u2} Cardinal.{u2} (Preorder.toHasLt.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
 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)] [_inst_4 : NoZeroSMulDivisors.{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))))) (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))))] [_inst_5 : Nontrivial.{u2} M], LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (Zero.toOfNat0.{succ u2} Cardinal.{u2} Cardinal.instZeroCardinal.{u2})) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
 Case conversion may be inaccurate. Consider using '#align rank_pos rank_posₓ'. -/
@@ -709,7 +709,7 @@ theorem rank_zero_iff : Module.rank R M = 0 ↔ Subsingleton M :=
 
 /- warning: rank_pos_iff_exists_ne_zero -> rank_pos_iff_exists_ne_zero is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_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))))] [_inst_5 : Nontrivial.{u1} R], Iff (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Exists.{succ u2} M (fun (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))))))))))
+  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))))] [_inst_5 : Nontrivial.{u1} R], Iff (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toHasLt.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Exists.{succ u2} M (fun (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))))))))))
 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)] [_inst_4 : NoZeroSMulDivisors.{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))))) (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))))] [_inst_5 : Nontrivial.{u1} R], Iff (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (Zero.toOfNat0.{succ u2} Cardinal.{u2} Cardinal.instZeroCardinal.{u2})) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Exists.{succ u2} M (fun (x : M) => Ne.{succ u2} M x (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)))))))))
 Case conversion may be inaccurate. Consider using '#align rank_pos_iff_exists_ne_zero rank_pos_iff_exists_ne_zeroₓ'. -/
@@ -721,7 +721,7 @@ theorem rank_pos_iff_exists_ne_zero : 0 < Module.rank R M ↔ ∃ x : M, x ≠ 0
 
 /- warning: rank_pos_iff_nontrivial -> rank_pos_iff_nontrivial is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_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))))] [_inst_5 : Nontrivial.{u1} R], Iff (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Nontrivial.{u2} M)
+  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))))] [_inst_5 : Nontrivial.{u1} R], Iff (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toHasLt.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Nontrivial.{u2} M)
 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)] [_inst_4 : NoZeroSMulDivisors.{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))))) (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))))] [_inst_5 : Nontrivial.{u1} R], Iff (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (Zero.toOfNat0.{succ u2} Cardinal.{u2} Cardinal.instZeroCardinal.{u2})) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Nontrivial.{u2} M)
 Case conversion may be inaccurate. Consider using '#align rank_pos_iff_nontrivial rank_pos_iff_nontrivialₓ'. -/
@@ -1136,7 +1136,7 @@ theorem Basis.card_le_card_of_submodule (N : Submodule R M) [Fintype ι] (b : Ba
 
 /- warning: basis.card_le_card_of_le -> Basis.card_le_card_of_le is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u3}} {ι' : Type.{u4}} {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4} {O : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4}, (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) N O) -> (forall [_inst_5 : Fintype.{u3} ι], (Basis.{u3, u1, u2} ι R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) O) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 O) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 O)) -> (forall [_inst_6 : Fintype.{u4} ι'], (Basis.{u4, u1, u2} ι' R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) N) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 N) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 N)) -> (LE.le.{0} Nat Nat.hasLe (Fintype.card.{u4} ι' _inst_6) (Fintype.card.{u3} ι _inst_5))))
+  forall {ι : Type.{u3}} {ι' : Type.{u4}} {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4} {O : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4}, (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) N O) -> (forall [_inst_5 : Fintype.{u3} ι], (Basis.{u3, u1, u2} ι R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) O) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 O) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 O)) -> (forall [_inst_6 : Fintype.{u4} ι'], (Basis.{u4, u1, u2} ι' R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) N) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 N) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 N)) -> (LE.le.{0} Nat Nat.hasLe (Fintype.card.{u4} ι' _inst_6) (Fintype.card.{u3} ι _inst_5))))
 but is expected to have type
   forall {ι : Type.{u3}} {ι' : Type.{u4}} {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4} {O : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4}, (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) N O) -> (forall [_inst_5 : Fintype.{u3} ι], (Basis.{u3, u1, u2} ι R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) x O)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 O) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 O)) -> (forall [_inst_6 : Fintype.{u4} ι'], (Basis.{u4, u1, u2} ι' R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) x N)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 N) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 N)) -> (LE.le.{0} Nat instLENat (Fintype.card.{u4} ι' _inst_6) (Fintype.card.{u3} ι _inst_5))))
 Case conversion may be inaccurate. Consider using '#align basis.card_le_card_of_le Basis.card_le_card_of_leₓ'. -/
@@ -1164,7 +1164,7 @@ theorem Basis.mk_eq_rank'.{m} (v : Basis ι R M) :
 
 /- warning: basis.nonempty_fintype_index_of_rank_lt_aleph_0 -> Basis.nonempty_fintype_index_of_rank_lt_aleph0 is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}}, (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Cardinal.aleph0.{u2}) -> (Nonempty.{succ u3} (Fintype.{u3} ι))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}}, (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toHasLt.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Cardinal.aleph0.{u2}) -> (Nonempty.{succ u3} (Fintype.{u3} ι))
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] [_inst_2 : StrongRankCondition.{u2} R (Ring.toSemiring.{u2} R _inst_1)] {M : Type.{u3}} [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] {ι : Type.{u1}}, (Basis.{u1, u2, u3} ι R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) -> (LT.lt.{succ u3} Cardinal.{u3} (Preorder.toLT.{succ u3} Cardinal.{u3} (PartialOrder.toPreorder.{succ u3} Cardinal.{u3} Cardinal.partialOrder.{u3})) (Module.rank.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) Cardinal.aleph0.{u3}) -> (Nonempty.{succ u1} (Fintype.{u1} ι))
 Case conversion may be inaccurate. Consider using '#align basis.nonempty_fintype_index_of_rank_lt_aleph_0 Basis.nonempty_fintype_index_of_rank_lt_aleph0ₓ'. -/
@@ -1175,17 +1175,21 @@ theorem Basis.nonempty_fintype_index_of_rank_lt_aleph0 {ι : Type _} (b : Basis
     Cardinal.lt_aleph0_iff_fintype] at h
 #align basis.nonempty_fintype_index_of_rank_lt_aleph_0 Basis.nonempty_fintype_index_of_rank_lt_aleph0
 
-#print Basis.fintypeIndexOfRankLtAleph0 /-
+/- warning: basis.fintype_index_of_rank_lt_aleph_0 -> Basis.fintypeIndexOfRankLtAleph0 is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}}, (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toHasLt.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Cardinal.aleph0.{u2}) -> (Fintype.{u3} ι)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}}, (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Cardinal.aleph0.{u2}) -> (Fintype.{u3} ι)
+Case conversion may be inaccurate. Consider using '#align basis.fintype_index_of_rank_lt_aleph_0 Basis.fintypeIndexOfRankLtAleph0ₓ'. -/
 /-- If a module has a finite dimension, all bases are indexed by a finite type. -/
 noncomputable def Basis.fintypeIndexOfRankLtAleph0 {ι : Type _} (b : Basis ι R M)
     (h : Module.rank R M < ℵ₀) : Fintype ι :=
   Classical.choice (b.nonempty_fintype_index_of_rank_lt_aleph0 h)
 #align basis.fintype_index_of_rank_lt_aleph_0 Basis.fintypeIndexOfRankLtAleph0
--/
 
 /- warning: basis.finite_index_of_rank_lt_aleph_0 -> Basis.finite_index_of_rank_lt_aleph0 is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}} {s : Set.{u3} ι}, (Basis.{u3, u1, u2} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Cardinal.aleph0.{u2}) -> (Set.Finite.{u3} ι s)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}} {s : Set.{u3} ι}, (Basis.{u3, u1, u2} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toHasLt.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Cardinal.aleph0.{u2}) -> (Set.Finite.{u3} ι s)
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] [_inst_2 : StrongRankCondition.{u2} R (Ring.toSemiring.{u2} R _inst_1)] {M : Type.{u3}} [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] {ι : Type.{u1}} {s : Set.{u1} ι}, (Basis.{u1, u2, u3} (Set.Elem.{u1} ι s) R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) -> (LT.lt.{succ u3} Cardinal.{u3} (Preorder.toLT.{succ u3} Cardinal.{u3} (PartialOrder.toPreorder.{succ u3} Cardinal.{u3} Cardinal.partialOrder.{u3})) (Module.rank.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) Cardinal.aleph0.{u3}) -> (Set.Finite.{u1} ι s)
 Case conversion may be inaccurate. Consider using '#align basis.finite_index_of_rank_lt_aleph_0 Basis.finite_index_of_rank_lt_aleph0ₓ'. -/
@@ -1216,7 +1220,7 @@ theorem rank_span_set {s : Set M} (hs : LinearIndependent R (fun x => x : s →
 
 /- warning: submodule.induction_on_rank -> Submodule.inductionOnRank is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u3}} {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_5 : IsDomain.{u1} R (Ring.toSemiring.{u1} R _inst_1)] [_inst_6 : Fintype.{u3} ι], (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (forall (P : (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> Sort.{u4}), (forall (N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), (forall (N' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) N' N) -> (forall (x : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) x N) -> (forall (c : R) (y : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) y N') -> (Eq.{succ u2} M (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_3)))))) (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_3)))) (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_3)))) (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_3)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) c x) y) (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_3))))))))) -> (Eq.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))))) -> (P N'))) -> (P N)) -> (forall (N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), P N))
+  forall {ι : Type.{u3}} {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_5 : IsDomain.{u1} R (Ring.toSemiring.{u1} R _inst_1)] [_inst_6 : Fintype.{u3} ι], (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (forall (P : (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> Sort.{u4}), (forall (N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), (forall (N' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) N' N) -> (forall (x : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) x N) -> (forall (c : R) (y : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) y N') -> (Eq.{succ u2} M (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_3)))))) (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_3)))) (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_3)))) (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_3)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) c x) y) (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_3))))))))) -> (Eq.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))))) -> (P N'))) -> (P N)) -> (forall (N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), P N))
 but is expected to have type
   forall {ι : Type.{u3}} {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_5 : IsDomain.{u1} R (Ring.toSemiring.{u1} R _inst_1)] [_inst_6 : Fintype.{u3} ι], (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (forall (P : (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> Sort.{u4}), (forall (N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), (forall (N' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) N' N) -> (forall (x : M), (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) x N) -> (forall (c : R) (y : M), (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) y N') -> (Eq.{succ u2} M (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_3)))))) (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_3))))) (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_3))))) (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_3))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) c x) y) (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_3)))))))) -> (Eq.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) -> (P N'))) -> (P N)) -> (forall (N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), P N))
 Case conversion may be inaccurate. Consider using '#align submodule.induction_on_rank Submodule.inductionOnRankₓ'. -/
@@ -1491,13 +1495,17 @@ variable [AddCommGroup V₁] [Module K V₁]
 
 variable {K V}
 
-#print Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0 /-
+/- warning: basis.finite_of_vector_space_index_of_rank_lt_aleph_0 -> Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0 is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)], (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toHasLt.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Cardinal.aleph0.{u2}) -> (Set.Finite.{u2} V (Basis.ofVectorSpaceIndex.{u2, u1} K V _inst_1 _inst_2 _inst_3))
+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)], (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Module.rank.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Cardinal.aleph0.{u2}) -> (Set.Finite.{u2} V (Basis.ofVectorSpaceIndex.{u2, u1} K V _inst_1 _inst_2 _inst_3))
+Case conversion may be inaccurate. Consider using '#align basis.finite_of_vector_space_index_of_rank_lt_aleph_0 Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0ₓ'. -/
 /-- If a vector space has a finite dimension, the index set of `basis.of_vector_space` is finite. -/
 theorem Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0 (h : Module.rank K V < ℵ₀) :
     (Basis.ofVectorSpaceIndex K V).Finite :=
   finite_def.2 <| (Basis.ofVectorSpace K V).nonempty_fintype_index_of_rank_lt_aleph0 h
 #align basis.finite_of_vector_space_index_of_rank_lt_aleph_0 Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0
--/
 
 #print rank_span_le /-
 -- TODO how far can we generalise this?
@@ -1511,7 +1519,12 @@ theorem rank_span_le (s : Set V) : Module.rank K (span K s) ≤ (#s) :=
 #align rank_span_le rank_span_le
 -/
 
-#print rank_span_of_finset /-
+/- warning: rank_span_of_finset -> rank_span_of_finset is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (s : Finset.{u2} V), LT.lt.{succ u2} Cardinal.{u2} (Preorder.toHasLt.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Module.rank.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s))) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s))) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)))) Cardinal.aleph0.{u2}
+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (s : Finset.{u2} V), LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Module.rank.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Finset.toSet.{u2} V s)))) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Finset.toSet.{u2} V s))) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Finset.toSet.{u2} V s)))) Cardinal.aleph0.{u2}
+Case conversion may be inaccurate. Consider using '#align rank_span_of_finset rank_span_of_finsetₓ'. -/
 theorem rank_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V)) < ℵ₀ :=
   calc
     Module.rank K (span K (↑s : Set V)) ≤ (#(↑s : Set V)) := rank_span_le ↑s
@@ -1519,7 +1532,6 @@ theorem rank_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V
     _ < ℵ₀ := Cardinal.nat_lt_aleph0 _
     
 #align rank_span_of_finset rank_span_of_finset
--/
 
 /- warning: rank_quotient_add_rank -> rank_quotient_add_rank is a dubious translation:
 lean 3 declaration is
@@ -1569,7 +1581,7 @@ open LinearMap
 
 /- warning: rank_add_rank_split -> rank_add_rank_split is a dubious translation:
 lean 3 declaration is
-  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} {V₂ : Type.{u2}} {V₃ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] [_inst_8 : AddCommGroup.{u2} V₂] [_inst_9 : Module.{u1, u2} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8)] [_inst_10 : AddCommGroup.{u2} V₃] [_inst_11 : Module.{u1, u2} K V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10)] (db : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) 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eb e)) -> (Exists.{succ u2} V₁ (fun (c : V₁) => And (Eq.{succ u2} V₂ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) cd c) d) (Eq.{succ u2} V₃ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11) => V₁ -> V₃) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₁ V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) ce c) e)))) -> (Eq.{succ (succ u2)} Cardinal.{u2} (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.rank.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7)) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_9) (Module.rank.{u1, u2} K V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_11)))
+  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} {V₂ : Type.{u2}} {V₃ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] [_inst_8 : AddCommGroup.{u2} V₂] [_inst_9 : Module.{u1, u2} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8)] [_inst_10 : AddCommGroup.{u2} V₃] [_inst_11 : Module.{u1, u2} K V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10)] (db : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (eb : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (cd : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (ce : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11), (LE.le.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Top.top.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _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 _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 _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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) db) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) eb))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (LinearMap.ker.{u1, u1, u2, u2, u2} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) cd) (Bot.bot.{u2} (Submodule.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Submodule.hasBot.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7))) -> (Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_3) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) db cd) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) eb ce)) -> (forall (d : V₂) (e : V₃), (Eq.{succ u2} V (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K 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(Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) => V₃ -> V) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) eb e)) -> (Exists.{succ u2} V₁ (fun (c : V₁) => And (Eq.{succ u2} V₂ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) cd c) d) (Eq.{succ u2} V₃ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11) => V₁ -> V₃) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₁ V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) ce c) e)))) -> (Eq.{succ (succ u2)} Cardinal.{u2} (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.rank.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7)) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_9) (Module.rank.{u1, u2} K V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_11)))
 but is expected to have type
   forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} {V₂ : Type.{u2}} {V₃ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] [_inst_8 : AddCommGroup.{u2} V₂] [_inst_9 : Module.{u1, u2} K V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8)] [_inst_10 : AddCommGroup.{u2} V₃] [_inst_11 : Module.{u1, u2} K V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10)] (db : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (eb : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (cd : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) 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K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) db) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V 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succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_9) (Module.rank.{u1, u2} K V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_11)))
 Case conversion may be inaccurate. Consider using '#align rank_add_rank_split rank_add_rank_splitₓ'. -/
@@ -1736,7 +1748,7 @@ theorem rank_le_one_iff : Module.rank K V ≤ 1 ↔ ∃ v₀ : V, ∀ v, ∃ r :
 
 /- warning: rank_submodule_le_one_iff -> rank_submodule_le_one_iff is a dubious translation:
 lean 3 declaration is
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+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (s : Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Iff (LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Module.rank.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) s) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 s) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 s)) (OfNat.ofNat.{succ u2} Cardinal.{u2} 1 (OfNat.mk.{succ u2} Cardinal.{u2} 1 (One.one.{succ u2} Cardinal.{u2} Cardinal.hasOne.{u2})))) (Exists.{succ u2} V (fun (v₀ : V) => Exists.{0} (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v₀ s) (fun (H : Membership.Mem.{u2, u2} V (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v₀ s) => LE.le.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) s (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) v₀)))))
 but is expected to have type
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (s : Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Iff (LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x s)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 s) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 s)) (OfNat.ofNat.{succ u2} Cardinal.{u2} 1 (One.toOfNat1.{succ u2} Cardinal.{u2} Cardinal.instOneCardinal.{u2}))) (Exists.{succ u2} V (fun (v₀ : V) => And (Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v₀ s) (LE.le.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) s (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) v₀)))))
 Case conversion may be inaccurate. Consider using '#align rank_submodule_le_one_iff rank_submodule_le_one_iffₓ'. -/
@@ -1766,7 +1778,7 @@ theorem rank_submodule_le_one_iff (s : Submodule K V) :
 
 /- warning: rank_submodule_le_one_iff' -> rank_submodule_le_one_iff' is a dubious translation:
 lean 3 declaration is
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (s : Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Iff (LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Module.rank.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) s) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 s) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 s)) (OfNat.ofNat.{succ u2} Cardinal.{u2} 1 (OfNat.mk.{succ u2} Cardinal.{u2} 1 (One.one.{succ u2} Cardinal.{u2} Cardinal.hasOne.{u2})))) (Exists.{succ u2} V (fun (v₀ : V) => LE.le.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) s (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) v₀))))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (s : Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Iff (LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Module.rank.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) s) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 s) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 s)) (OfNat.ofNat.{succ u2} Cardinal.{u2} 1 (OfNat.mk.{succ u2} Cardinal.{u2} 1 (One.one.{succ u2} Cardinal.{u2} Cardinal.hasOne.{u2})))) (Exists.{succ u2} V (fun (v₀ : V) => LE.le.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) s (Submodule.span.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) v₀))))
 but is expected to have type
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (s : Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Iff (LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x s)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 s) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 s)) (OfNat.ofNat.{succ u2} Cardinal.{u2} 1 (One.toOfNat1.{succ u2} Cardinal.{u2} Cardinal.instOneCardinal.{u2}))) (Exists.{succ u2} V (fun (v₀ : V) => LE.le.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) s (Submodule.span.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) v₀))))
 Case conversion may be inaccurate. Consider using '#align rank_submodule_le_one_iff' rank_submodule_le_one_iff'ₓ'. -/

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

@@ -1418,7 +1418,7 @@ variable [Fintype η]
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] {V : Type.{u1}} {η : Type.{u1}} [_inst_16 : Fintype.{u1} η] [_inst_17 : AddCommGroup.{u1} V] [_inst_18 : Module.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17)] [_inst_19 : Module.Free.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u1, u1} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17)) (Pi.Function.module.{u1, u1, u1} η K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18)) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) (Fintype.card.{u1} η _inst_16)) (Module.rank.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] {V : Type.{u1}} {η : Type.{u1}} [_inst_16 : Fintype.{u1} η] [_inst_17 : AddCommGroup.{u1} V] [_inst_18 : Module.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17)] [_inst_19 : Module.Free.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u1, u1} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17)) (Pi.module.{u1, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13034 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17) (fun (i : η) => _inst_18))) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} (Fintype.card.{u1} η _inst_16)) (Module.rank.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18))
+  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] {V : Type.{u1}} {η : Type.{u1}} [_inst_16 : Fintype.{u1} η] [_inst_17 : AddCommGroup.{u1} V] [_inst_18 : Module.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17)] [_inst_19 : Module.Free.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u1, u1} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17)) (Pi.module.{u1, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.12860 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17) (fun (i : η) => _inst_18))) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} (Fintype.card.{u1} η _inst_16)) (Module.rank.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18))
 Case conversion may be inaccurate. Consider using '#align rank_fun rank_funₓ'. -/
 theorem rank_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] [Module.Free K V] :
     Module.rank K (η → V) = Fintype.card η * Module.rank K V := by
@@ -1429,7 +1429,7 @@ theorem rank_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] [Mod
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {η : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] [_inst_15 : Fintype.{u3} η], Eq.{succ (succ (max u3 u2))} Cardinal.{max u3 u2} (Module.rank.{u1, max u3 u2} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u3, u2} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3)) (Pi.Function.module.{u3, u1, u2} η K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)) (HMul.hMul.{succ (max u3 u2), succ (max u3 u2), succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.{max u3 u2} Cardinal.{max u3 u2} (instHMul.{succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.hasMul.{max u3 u2}) ((fun (a : Type) (b : Type.{succ (max u3 u2)}) [self : HasLiftT.{1, succ (succ (max u3 u2))} a b] => self.0) Nat Cardinal.{max u3 u2} (HasLiftT.mk.{1, succ (succ (max u3 u2))} Nat Cardinal.{max u3 u2} (CoeTCₓ.coe.{1, succ (succ (max u3 u2))} Nat Cardinal.{max u3 u2} (Nat.castCoe.{succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.hasNatCast.{max u3 u2}))) (Fintype.card.{u3} η _inst_15)) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {η : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] [_inst_15 : Fintype.{u3} η], Eq.{max (succ (succ u3)) (succ (succ u2))} Cardinal.{max u3 u2} (Module.rank.{u1, max u3 u2} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u3, u2} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3)) (Pi.module.{u3, u2, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13168 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (fun (i : η) => _inst_4))) (HMul.hMul.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.{max u2 u3} Cardinal.{max u3 u2} (instHMul.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instMulCardinal.{max u3 u2}) (Nat.cast.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instNatCastCardinal.{max u3 u2} (Fintype.card.{u3} η _inst_15)) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)))
+  forall {K : Type.{u1}} {V : Type.{u2}} {η : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] [_inst_15 : Fintype.{u3} η], Eq.{max (succ (succ u3)) (succ (succ u2))} Cardinal.{max u3 u2} (Module.rank.{u1, max u3 u2} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u3, u2} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3)) (Pi.module.{u3, u2, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.12994 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (fun (i : η) => _inst_4))) (HMul.hMul.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.{max u2 u3} Cardinal.{max u3 u2} (instHMul.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instMulCardinal.{max u3 u2}) (Nat.cast.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instNatCastCardinal.{max u3 u2} (Fintype.card.{u3} η _inst_15)) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)))
 Case conversion may be inaccurate. Consider using '#align rank_fun_eq_lift_mul rank_fun_eq_lift_mulₓ'. -/
 theorem rank_fun_eq_lift_mul :
     Module.rank K (η → V) =
@@ -1441,7 +1441,7 @@ theorem rank_fun_eq_lift_mul :
 lean 3 declaration is
   forall {K : Type.{u1}} {η : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_15 : Fintype.{u2} η], Eq.{succ (succ (max u2 u1))} Cardinal.{max u2 u1} (Module.rank.{u1, max u2 u1} K (η -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => K) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.Function.module.{u2, u1, u1} η K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) ((fun (a : Type) (b : Type.{succ (max u2 u1)}) [self : HasLiftT.{1, succ (succ (max u2 u1))} a b] => self.0) Nat Cardinal.{max u2 u1} (HasLiftT.mk.{1, succ (succ (max u2 u1))} Nat Cardinal.{max u2 u1} (CoeTCₓ.coe.{1, succ (succ (max u2 u1))} Nat Cardinal.{max u2 u1} (Nat.castCoe.{succ (max u2 u1)} Cardinal.{max u2 u1} Cardinal.hasNatCast.{max u2 u1}))) (Fintype.card.{u2} η _inst_15))
 but is expected to have type
-  forall {K : Type.{u1}} {η : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_15 : Fintype.{u2} η], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (η -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => K) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{u2, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13315 : η) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : η) => Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) (Nat.cast.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instNatCastCardinal.{max u1 u2} (Fintype.card.{u2} η _inst_15))
+  forall {K : Type.{u1}} {η : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_15 : Fintype.{u2} η], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (η -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => K) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{u2, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13136 : η) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : η) => Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) (Nat.cast.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instNatCastCardinal.{max u1 u2} (Fintype.card.{u2} η _inst_15))
 Case conversion may be inaccurate. Consider using '#align rank_fun' rank_fun'ₓ'. -/
 theorem rank_fun' : Module.rank K (η → K) = Fintype.card η := by
   rw [rank_fun_eq_lift_mul, rank_self, Cardinal.lift_one, mul_one, Cardinal.natCast_inj]
@@ -1451,7 +1451,7 @@ theorem rank_fun' : Module.rank K (η → K) = Fintype.card η := by
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K ((Fin n) -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.Function.module.{0, u1, u1} (Fin n) K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K ((Fin n) -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13456 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)
+  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K ((Fin n) -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13271 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)
 Case conversion may be inaccurate. Consider using '#align rank_fin_fun rank_fin_funₓ'. -/
 theorem rank_fin_fun (n : ℕ) : Module.rank K (Fin n → K) = n := by simp [rank_fun']
 #align rank_fin_fun rank_fin_fun
@@ -1462,7 +1462,7 @@ end Fintype
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) ((fun (a : Type) (b : Type.{succ u2}) [self : HasLiftT.{1, succ (succ u2)} a b] => self.0) Nat Cardinal.{u2} (HasLiftT.mk.{1, succ (succ u2)} Nat Cardinal.{u2} (CoeTCₓ.coe.{1, succ (succ u2)} Nat Cardinal.{u2} (Nat.castCoe.{succ u2} Cardinal.{u2} Cardinal.hasNatCast.{u2}))) n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (finDimVectorspaceEquiv._proof_1.{u1} K _inst_1) (finDimVectorspaceEquiv._proof_2.{u1} K _inst_1) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.Function.module.{0, u1, u1} (Fin n) K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) (Nat.cast.{succ u2} Cardinal.{u2} Cardinal.instNatCastCardinal.{u2} n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13545 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1))))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) (Nat.cast.{succ u2} Cardinal.{u2} Cardinal.instNatCastCardinal.{u2} n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13354 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1))))
 Case conversion may be inaccurate. Consider using '#align fin_dim_vectorspace_equiv finDimVectorspaceEquivₓ'. -/
 -- TODO: merge with the `finrank` content
 /-- An `n`-dimensional `K`-vector space is equivalent to `fin n → K`. -/

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

@@ -142,9 +142,9 @@ theorem LinearMap.lift_rank_le_of_injective (f : M →ₗ[R] M') (i : Injective
     Cardinal.lift.{v'} (Module.rank R M) ≤ Cardinal.lift.{v} (Module.rank R M') :=
   by
   dsimp [Module.rank]
-  rw [Cardinal.lift_supᵢ (Cardinal.bddAbove_range.{v', v'} _),
-    Cardinal.lift_supᵢ (Cardinal.bddAbove_range.{v, v} _)]
-  apply csupᵢ_mono' (Cardinal.bddAbove_range.{v', v} _)
+  rw [Cardinal.lift_iSup (Cardinal.bddAbove_range.{v', v'} _),
+    Cardinal.lift_iSup (Cardinal.bddAbove_range.{v, v} _)]
+  apply ciSup_mono' (Cardinal.bddAbove_range.{v', v} _)
   rintro ⟨s, li⟩
   refine' ⟨⟨f '' s, _⟩, cardinal.lift_mk_le'.mpr ⟨(Equiv.Set.image f s i).toEmbedding⟩⟩
   exact (li.map' _ <| linear_map.ker_eq_bot.mpr i).image
@@ -171,7 +171,7 @@ theorem rank_le {n : ℕ}
     (H : ∀ s : Finset M, (LinearIndependent R fun i : s => (i : M)) → s.card ≤ n) :
     Module.rank R M ≤ n := by
   rw [Module.rank]
-  apply csupᵢ_le'
+  apply ciSup_le'
   rintro ⟨s, li⟩
   exact linearIndependent_bounded_of_finset_linearIndependent_bounded H _ li
 #align rank_le rank_le
@@ -186,13 +186,13 @@ theorem lift_rank_range_le (f : M →ₗ[R] M') :
     Cardinal.lift.{v} (Module.rank R f.range) ≤ Cardinal.lift.{v'} (Module.rank R M) :=
   by
   dsimp [Module.rank]
-  rw [Cardinal.lift_supᵢ (Cardinal.bddAbove_range.{v', v'} _)]
-  apply csupᵢ_le'
+  rw [Cardinal.lift_iSup (Cardinal.bddAbove_range.{v', v'} _)]
+  apply ciSup_le'
   rintro ⟨s, li⟩
   apply le_trans
   swap
   apply cardinal.lift_le.mpr
-  refine' le_csupᵢ (Cardinal.bddAbove_range.{v, v} _) ⟨range_splitting f '' s, _⟩
+  refine' le_ciSup (Cardinal.bddAbove_range.{v, v} _) ⟨range_splitting f '' s, _⟩
   · apply LinearIndependent.of_comp f.range_restrict
     convert li.comp (Equiv.Set.rangeSplittingImageEquiv f s) (Equiv.injective _) using 1
   · exact (cardinal.lift_mk_eq'.mpr ⟨Equiv.Set.rangeSplittingImageEquiv f s⟩).ge
@@ -356,7 +356,7 @@ theorem cardinal_lift_le_rank_of_linearIndependent.{m} {ι : Type w} {v : ι →
   · simp only [Cardinal.lift_le, Module.rank]
     apply le_trans
     swap
-    exact le_csupᵢ (Cardinal.bddAbove_range.{v, v} _) ⟨range v, hv.coe_range⟩
+    exact le_ciSup (Cardinal.bddAbove_range.{v, v} _) ⟨range v, hv.coe_range⟩
     exact le_rfl
 #align cardinal_lift_le_rank_of_linear_independent cardinal_lift_le_rank_of_linearIndependent
 
@@ -394,7 +394,7 @@ theorem rank_punit : Module.rank R PUnit = 0 :=
   by
   apply le_bot_iff.mp
   rw [Module.rank]
-  apply csupᵢ_le'
+  apply ciSup_le'
   rintro ⟨s, li⟩
   apply le_bot_iff.mpr
   apply cardinal.mk_emptyc_iff.mpr
@@ -499,9 +499,9 @@ def basisFintypeOfFiniteSpans (w : Set M) [Fintype w] (s : span R w = ⊤) {ι :
 
 /- warning: union_support_maximal_linear_independent_eq_range_basis -> union_support_maximal_linearIndependent_eq_range_basis is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_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_8 : Nontrivial.{u1} R] {ι : Type.{u3}} (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {κ : Type.{u4}} (v : κ -> M) (i : LinearIndependent.{u4, u1, u2} κ R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), (LinearIndependent.Maximal.{u1, u2, u4} κ R (Ring.toSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 v i) -> (Eq.{succ u3} (Set.{u3} ι) (Set.unionᵢ.{u3, succ u4} ι κ (fun (k : κ) => (fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Finset.{u3} ι) (Set.{u3} ι) (HasLiftT.mk.{succ u3, succ u3} (Finset.{u3} ι) (Set.{u3} ι) (CoeTCₓ.coe.{succ u3, succ u3} (Finset.{u3} ι) (Set.{u3} ι) (Finset.Set.hasCoeT.{u3} ι))) (Finsupp.support.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => M -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Basis.repr.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b) (v k))))) (Set.univ.{u3} ι))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_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_8 : Nontrivial.{u1} R] {ι : Type.{u3}} (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {κ : Type.{u4}} (v : κ -> M) (i : LinearIndependent.{u4, u1, u2} κ R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), (LinearIndependent.Maximal.{u1, u2, u4} κ R (Ring.toSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 v i) -> (Eq.{succ u3} (Set.{u3} ι) (Set.iUnion.{u3, succ u4} ι κ (fun (k : κ) => (fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (Finset.{u3} ι) (Set.{u3} ι) (HasLiftT.mk.{succ u3, succ u3} (Finset.{u3} ι) (Set.{u3} ι) (CoeTCₓ.coe.{succ u3, succ u3} (Finset.{u3} ι) (Set.{u3} ι) (Finset.Set.hasCoeT.{u3} ι))) (Finsupp.support.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => M -> (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Basis.repr.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b) (v k))))) (Set.univ.{u3} ι))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_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_8 : Nontrivial.{u1} R] {ι : Type.{u3}} (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {κ : Type.{u4}} (v : κ -> M) (i : LinearIndependent.{u4, u1, u2} κ R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), (LinearIndependent.Maximal.{u1, u2, u4} κ R (Ring.toSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 v i) -> (Eq.{succ u3} (Set.{u3} ι) (Set.unionᵢ.{u3, succ u4} ι κ (fun (k : κ) => Finset.toSet.{u3} ι (Finsupp.support.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b) (v k))))) (Set.univ.{u3} ι))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_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_8 : Nontrivial.{u1} R] {ι : Type.{u3}} (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {κ : Type.{u4}} (v : κ -> M) (i : LinearIndependent.{u4, u1, u2} κ R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), (LinearIndependent.Maximal.{u1, u2, u4} κ R (Ring.toSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 v i) -> (Eq.{succ u3} (Set.{u3} ι) (Set.iUnion.{u3, succ u4} ι κ (fun (k : κ) => Finset.toSet.{u3} ι (Finsupp.support.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b) (v k))))) (Set.univ.{u3} ι))
 Case conversion may be inaccurate. Consider using '#align union_support_maximal_linear_independent_eq_range_basis union_support_maximal_linearIndependent_eq_range_basisₓ'. -/
 -- From [Les familles libres maximales d'un module ont-elles le meme cardinal?][lazarus1973]
 /-- Over any ring `R`, if `b` is a basis for a module `M`,
@@ -644,7 +644,7 @@ theorem rank_subsingleton [Subsingleton R] : Module.rank R M = 1 :=
   haveI := Module.subsingleton R M
   have : Nonempty { s : Set M // LinearIndependent R (coe : s → M) } :=
     ⟨⟨∅, linearIndependent_empty _ _⟩⟩
-  rw [Module.rank, csupᵢ_eq_of_forall_le_of_forall_lt_exists_gt]
+  rw [Module.rank, ciSup_eq_of_forall_le_of_forall_lt_exists_gt]
   · rintro ⟨s, hs⟩
     rw [Cardinal.mk_le_one_iff_set_subsingleton]
     apply subsingleton_of_subsingleton
@@ -876,7 +876,7 @@ theorem Basis.le_span {J : Set M} (v : Basis ι R M) (hJ : span R J = ⊤) : (#r
     refine' le_of_not_lt fun IJ => _
     suffices (#⋃ j, S' j) < (#range v) by exact not_le_of_lt this ⟨Set.embeddingOfSubset _ _ hs⟩
     refine'
-      lt_of_le_of_lt (le_trans Cardinal.mk_unionᵢ_le_sum_mk (Cardinal.sum_le_sum _ (fun _ => ℵ₀) _))
+      lt_of_le_of_lt (le_trans Cardinal.mk_iUnion_le_sum_mk (Cardinal.sum_le_sum _ (fun _ => ℵ₀) _))
         _
     · exact fun j => (Cardinal.lt_aleph0_of_finite _).le
     · simpa
@@ -1078,14 +1078,14 @@ theorem Basis.mk_eq_rank'' {ι : Type v} (v : Basis ι R M) : (#ι) = Module.ran
   apply le_antisymm
   · trans
     swap
-    apply le_csupᵢ (Cardinal.bddAbove_range.{v, v} _)
+    apply le_ciSup (Cardinal.bddAbove_range.{v, v} _)
     exact
       ⟨Set.range v, by
         convert v.reindex_range.linear_independent
         ext
         simp⟩
     exact (Cardinal.mk_range_eq v v.injective).ge
-  · apply csupᵢ_le'
+  · apply ciSup_le'
     rintro ⟨s, li⟩
     apply linearIndependent_le_basis v _ li
 #align basis.mk_eq_rank'' Basis.mk_eq_rank''

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

@@ -136,7 +136,7 @@ variable {M₁ : Type v} [AddCommGroup M₁] [Module R M₁]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Injective.{succ u2, succ u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ (max u2 u3)} Cardinal.{max u2 u3} Cardinal.hasLe.{max u2 u3} (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Cardinal.lift.{u2, u3} (Module.rank.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Injective.{succ u2, succ u3} M M' (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) f)) -> (LE.le.{max (succ u2) (succ u3)} Cardinal.{max u2 u3} Cardinal.instLECardinal.{max u2 u3} (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Cardinal.lift.{u2, u3} (Module.rank.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Injective.{succ u2, succ u3} M M' (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{max (succ u2) (succ u3)} Cardinal.{max u2 u3} Cardinal.instLECardinal.{max u2 u3} (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Cardinal.lift.{u2, u3} (Module.rank.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)))
 Case conversion may be inaccurate. Consider using '#align linear_map.lift_rank_le_of_injective LinearMap.lift_rank_le_of_injectiveₓ'. -/
 theorem LinearMap.lift_rank_le_of_injective (f : M →ₗ[R] M') (i : Injective f) :
     Cardinal.lift.{v'} (Module.rank R M) ≤ Cardinal.lift.{v} (Module.rank R M') :=
@@ -154,7 +154,7 @@ theorem LinearMap.lift_rank_le_of_injective (f : M →ₗ[R] M') (i : Injective
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Injective.{succ u2, succ u2} M M₁ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) => M -> M₁) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.rank.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Injective.{succ u2, succ u2} M M₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) f)) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.rank.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Injective.{succ u2, succ u2} M M₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.rank.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7))
 Case conversion may be inaccurate. Consider using '#align linear_map.rank_le_of_injective LinearMap.rank_le_of_injectiveₓ'. -/
 theorem LinearMap.rank_le_of_injective (f : M →ₗ[R] M₁) (i : Injective f) :
     Module.rank R M ≤ Module.rank R M₁ :=
@@ -180,7 +180,7 @@ theorem rank_le {n : ℕ}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), LE.le.{succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.hasLe.{max u3 u2} (Cardinal.lift.{u2, u3} (Module.rank.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)))) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), LE.le.{max (succ u2) (succ u3)} Cardinal.{max u3 u2} Cardinal.instLECardinal.{max u2 u3} (Cardinal.lift.{u2, u3} (Module.rank.{u1, u3} R (Subtype.{succ u3} M' (fun (x : M') => Membership.mem.{u3, u3} M' (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) x (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)))) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), LE.le.{max (succ u2) (succ u3)} Cardinal.{max u3 u2} Cardinal.instLECardinal.{max u2 u3} (Cardinal.lift.{u2, u3} (Module.rank.{u1, u3} R (Subtype.{succ u3} M' (fun (x : M') => Membership.mem.{u3, u3} M' (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) x (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)))) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))
 Case conversion may be inaccurate. Consider using '#align lift_rank_range_le lift_rank_range_leₓ'. -/
 theorem lift_rank_range_le (f : M →ₗ[R] M') :
     Cardinal.lift.{v} (Module.rank R f.range) ≤ Cardinal.lift.{v'} (Module.rank R M) :=
@@ -202,7 +202,7 @@ theorem lift_rank_range_le (f : M →ₗ[R] M') :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Module.rank.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) M₁ (Submodule.setLike.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7)) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} R (Subtype.{succ u2} M₁ (fun (x : M₁) => Membership.mem.{u2, u2} M₁ (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) M₁ (Submodule.setLike.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7)) x (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} R (Subtype.{succ u2} M₁ (fun (x : M₁) => Membership.mem.{u2, u2} M₁ (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) M₁ (Submodule.setLike.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7)) x (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
 Case conversion may be inaccurate. Consider using '#align rank_range_le rank_range_leₓ'. -/
 theorem rank_range_le (f : M →ₗ[R] M₁) : Module.rank R f.range ≤ Module.rank R M := by
   simpa using lift_rank_range_le f
@@ -212,7 +212,7 @@ theorem rank_range_le (f : M →ₗ[R] M₁) : Module.rank R f.range ≤ Module.
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), LE.le.{succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.hasLe.{max u3 u2} (Cardinal.lift.{u2, u3} (Module.rank.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f p)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f p)) (Submodule.module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f p)))) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} 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)) p) (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 p) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), LE.le.{max (succ u2) (succ u3)} Cardinal.{max u3 u2} Cardinal.instLECardinal.{max u2 u3} (Cardinal.lift.{u2, u3} (Module.rank.{u1, u3} R (Subtype.{succ u3} M' (fun (x : M') => Membership.mem.{u3, u3} M' (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) x (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) f p))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) f p)) (Submodule.module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) f p)))) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_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 p)) (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 p) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), LE.le.{max (succ u2) (succ u3)} Cardinal.{max u3 u2} Cardinal.instLECardinal.{max u2 u3} (Cardinal.lift.{u2, u3} (Module.rank.{u1, u3} R (Subtype.{succ u3} M' (fun (x : M') => Membership.mem.{u3, u3} M' (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5)) x (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f p))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f p)) (Submodule.module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f p)))) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_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 p)) (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 p) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p)))
 Case conversion may be inaccurate. Consider using '#align lift_rank_map_le lift_rank_map_leₓ'. -/
 theorem lift_rank_map_le (f : M →ₗ[R] M') (p : Submodule R M) :
     Cardinal.lift.{v} (Module.rank R (p.map f)) ≤ Cardinal.lift.{v'} (Module.rank R p) :=
@@ -225,7 +225,7 @@ theorem lift_rank_map_le (f : M →ₗ[R] M') (p : Submodule R M) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Module.rank.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) M₁ (Submodule.setLike.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7)) (Submodule.map.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f p)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (Submodule.map.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f p)) (Submodule.module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (Submodule.map.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f p))) (Module.rank.{u1, u2} 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)) p) (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 p) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} R (Subtype.{succ u2} M₁ (fun (x : M₁) => Membership.mem.{u2, u2} M₁ (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) M₁ (Submodule.setLike.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7)) x (Submodule.map.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) f p))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (Submodule.map.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) f p)) (Submodule.module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (Submodule.map.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) f p))) (Module.rank.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_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 p)) (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 p) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} R (Subtype.{succ u2} M₁ (fun (x : M₁) => Membership.mem.{u2, u2} M₁ (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) M₁ (Submodule.setLike.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7)) x (Submodule.map.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f p))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (Submodule.map.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f p)) (Submodule.module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (Submodule.map.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f p))) (Module.rank.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_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 p)) (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 p) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p))
 Case conversion may be inaccurate. Consider using '#align rank_map_le rank_map_leₓ'. -/
 theorem rank_map_le (f : M →ₗ[R] M₁) (p : Submodule R M) :
     Module.rank R (p.map f) ≤ Module.rank R p := by simpa using lift_rank_map_le f p
@@ -266,7 +266,7 @@ theorem LinearEquiv.rank_eq (f : M ≃ₗ[R] M₁) : Module.rank R M = Module.ra
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Injective.{succ u2, succ u2} M M₁ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) => M -> M₁) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.rank.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) M₁ (Submodule.setLike.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7)) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Injective.{succ u2, succ u2} M M₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) f)) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.rank.{u1, u2} R (Subtype.{succ u2} M₁ (fun (x : M₁) => Membership.mem.{u2, u2} M₁ (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) M₁ (Submodule.setLike.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7)) x (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Injective.{succ u2, succ u2} M M₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.rank.{u1, u2} R (Subtype.{succ u2} M₁ (fun (x : M₁) => Membership.mem.{u2, u2} M₁ (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) M₁ (Submodule.setLike.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7)) x (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))))
 Case conversion may be inaccurate. Consider using '#align rank_eq_of_injective rank_eq_of_injectiveₓ'. -/
 theorem rank_eq_of_injective (f : M →ₗ[R] M₁) (h : Injective f) :
     Module.rank R M = Module.rank R f.range :=
@@ -277,7 +277,7 @@ theorem rank_eq_of_injective (f : M →ₗ[R] M₁) (h : Injective f) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) M₁ (Submodule.setLike.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7)) (Submodule.map.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) 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 but is expected to have type
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_inst_2) _inst_3), Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} R (Subtype.{succ u2} M₁ (fun (x : M₁) => Membership.mem.{u2, u2} M₁ (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) M₁ (Submodule.setLike.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7)) x (Submodule.map.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 f) p))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (Submodule.map.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 f) p)) (Submodule.module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (Submodule.map.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 f) p))) (Module.rank.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_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 p)) (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 p) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (p : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} R (Subtype.{succ u2} M₁ (fun (x : M₁) => Membership.mem.{u2, u2} M₁ (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) M₁ (Submodule.setLike.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7)) x (Submodule.map.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 f) p))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (Submodule.map.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 f) p)) (Submodule.module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7 (Submodule.map.{u1, u1, u2, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 f) p))) (Module.rank.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_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 p)) (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 p) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p))
 Case conversion may be inaccurate. Consider using '#align linear_equiv.rank_map_eq LinearEquiv.rank_map_eqₓ'. -/
 /-- Pushforwards of submodules along a `linear_equiv` have the same dimension. -/
 theorem LinearEquiv.rank_map_eq (f : M ≃ₗ[R] M₁) (p : Submodule R M) :
@@ -306,7 +306,7 @@ variable {R M}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{succ u2, succ u3} M M' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) => M -> M') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Eq.{succ (succ u3)} Cardinal.{u3} (Module.rank.{u1, u3} R (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) Type.{u3} 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(Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' 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_inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Module.rank.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5))
 but is expected to have type
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(AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) f)) -> (Eq.{succ (succ u3)} Cardinal.{u3} (Module.rank.{u1, u3} R (Subtype.{succ u3} M' (fun (x : M') => Membership.mem.{u3, u3} M' (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) 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(Ring.toNonAssocRing.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Module.rank.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M' : Type.{u3}} [_inst_4 : AddCommGroup.{u3} M'] [_inst_5 : Module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4)] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5), (Function.Surjective.{succ u2, succ u3} M M' (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Eq.{succ (succ u3)} Cardinal.{u3} (Module.rank.{u1, u3} R (Subtype.{succ u3} M' (fun (x : M') => Membership.mem.{u3, u3} M' (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5) M' (Submodule.setLike.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) 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(Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f)) (Submodule.module.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5 (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M' (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u3} R R M M' (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_3 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) f))) (Module.rank.{u1, u3} R M' (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M' _inst_4) _inst_5))
 Case conversion may be inaccurate. Consider using '#align rank_range_of_surjective rank_range_of_surjectiveₓ'. -/
 theorem rank_range_of_surjective (f : M →ₗ[R] M') (h : Surjective f) :
     Module.rank R f.range = Module.rank R M' := by rw [LinearMap.range_eq_top.2 h, rank_top]
@@ -324,7 +324,7 @@ theorem rank_submodule_le (s : Submodule R M) : Module.rank R s ≤ Module.rank
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} M M₁ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) => M -> M₁) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Module.rank.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} M M₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))) f)) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {M₁ : Type.{u2}} [_inst_6 : AddCommGroup.{u2} M₁] [_inst_7 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} M M₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M₁ (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M₁ (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.instLECardinal.{u2} (Module.rank.{u1, u2} R M₁ (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_6) _inst_7) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))
 Case conversion may be inaccurate. Consider using '#align linear_map.rank_le_of_surjective LinearMap.rank_le_of_surjectiveₓ'. -/
 theorem LinearMap.rank_le_of_surjective (f : M →ₗ[R] M₁) (h : Surjective f) :
     Module.rank R M₁ ≤ Module.rank R M :=
@@ -1236,7 +1236,7 @@ def Submodule.inductionOnRank [IsDomain R] [Fintype ι] (b : Basis ι R M)
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_5 : CommRing.{u1} R] [_inst_6 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))] [_inst_7 : Ring.{u2} S] [_inst_8 : IsDomain.{u2} S (Ring.toSemiring.{u2} S _inst_7)] [_inst_9 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S _inst_7)] {n : Type.{u3}} {m : Type.{u4}} [_inst_10 : Fintype.{u3} n] [_inst_11 : Fintype.{u4} m], (Basis.{u3, u1, u2} n R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (AddCommGroup.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toAddCommGroup.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S _inst_7)))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S _inst_7) _inst_9)) -> (forall {I : Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_7)}, (Ne.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_7)) I (Bot.bot.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_7)) (Submodule.hasBot.{u2, u2} S S (Ring.toSemiring.{u2} S _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_7)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S _inst_7))))) -> (Basis.{u4, u1, u2} m R (coeSort.{succ u2, succ (succ u2)} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S _inst_7)) S (Submodule.setLike.{u2, u2} S S (Ring.toSemiring.{u2} S _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_7)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S _inst_7)))) I) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (Submodule.addCommMonoid.{u2, u2} S S (Ring.toSemiring.{u2} S _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_7)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S _inst_7)) I) (Submodule.module'.{u1, u2, u2} R S S (Ring.toSemiring.{u2} S _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_7)))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S _inst_7)) I (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_7))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_7))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_7))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_7)))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S _inst_7) _inst_9))))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S _inst_7) _inst_9) (IsScalarTower.right.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S _inst_7) _inst_9))) -> (Eq.{1} Nat (Fintype.card.{u4} m _inst_11) (Fintype.card.{u3} n _inst_10)))
 but is expected to have type
-  forall {R : Type.{u4}} {S : Type.{u3}} [_inst_5 : CommRing.{u4} R] [_inst_6 : StrongRankCondition.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_5))] [_inst_7 : Ring.{u3} S] [_inst_8 : IsDomain.{u3} S (Ring.toSemiring.{u3} S _inst_7)] [_inst_9 : Algebra.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_5) (Ring.toSemiring.{u3} S _inst_7)] {n : Type.{u2}} {m : Type.{u1}} [_inst_10 : Fintype.{u2} n] [_inst_11 : Fintype.{u1} m], (Basis.{u2, u4, u3} n R S (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonUnitalNonAssocRing.{u3} S (Ring.toNonAssocRing.{u3} S _inst_7)))) (Algebra.toModule.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_5) (Ring.toSemiring.{u3} S _inst_7) _inst_9)) -> (forall {I : Ideal.{u3} S (Ring.toSemiring.{u3} S _inst_7)}, (Ne.{succ u3} (Ideal.{u3} S (Ring.toSemiring.{u3} S _inst_7)) I (Bot.bot.{u3} (Ideal.{u3} S (Ring.toSemiring.{u3} S _inst_7)) (Submodule.instBotSubmodule.{u3, u3} S S (Ring.toSemiring.{u3} S _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_7)))) (Semiring.toModule.{u3} S (Ring.toSemiring.{u3} S _inst_7))))) -> (Basis.{u1, u4, u3} m R (Subtype.{succ u3} S (fun (x : S) => Membership.mem.{u3, u3} S (Ideal.{u3} S (Ring.toSemiring.{u3} S _inst_7)) (SetLike.instMembership.{u3, u3} (Ideal.{u3} S (Ring.toSemiring.{u3} S _inst_7)) S (Submodule.setLike.{u3, u3} S S (Ring.toSemiring.{u3} S _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_7)))) (Semiring.toModule.{u3} S (Ring.toSemiring.{u3} S _inst_7)))) x I)) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_5)) (Submodule.addCommMonoid.{u3, u3} S S (Ring.toSemiring.{u3} S _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_7)))) (Semiring.toModule.{u3} S (Ring.toSemiring.{u3} S _inst_7)) I) (Submodule.module'.{u4, u3, u3} R S S (Ring.toSemiring.{u3} S _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_7)))) (Semiring.toModule.{u3} S (Ring.toSemiring.{u3} S _inst_7)) I (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_5)) (Algebra.toSMul.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_5) (Ring.toSemiring.{u3} S _inst_7) _inst_9) (Algebra.toModule.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_5) (Ring.toSemiring.{u3} S _inst_7) _inst_9) (IsScalarTower.right.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_5) (Ring.toSemiring.{u3} S _inst_7) _inst_9))) -> (Eq.{1} Nat (Fintype.card.{u1} m _inst_11) (Fintype.card.{u2} n _inst_10)))
+  forall {R : Type.{u4}} {S : Type.{u3}} [_inst_5 : CommRing.{u4} R] [_inst_6 : StrongRankCondition.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5))] [_inst_7 : Ring.{u3} S] [_inst_8 : IsDomain.{u3} S (Ring.toSemiring.{u3} S _inst_7)] [_inst_9 : Algebra.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_5) (Ring.toSemiring.{u3} S _inst_7)] {n : Type.{u2}} {m : Type.{u1}} [_inst_10 : Fintype.{u2} n] [_inst_11 : Fintype.{u1} m], (Basis.{u2, u4, u3} n R S (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonUnitalNonAssocRing.{u3} S (Ring.toNonAssocRing.{u3} S _inst_7)))) (Algebra.toModule.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_5) (Ring.toSemiring.{u3} S _inst_7) _inst_9)) -> (forall {I : Ideal.{u3} S (Ring.toSemiring.{u3} S _inst_7)}, (Ne.{succ u3} (Ideal.{u3} S (Ring.toSemiring.{u3} S _inst_7)) I (Bot.bot.{u3} (Ideal.{u3} S (Ring.toSemiring.{u3} S _inst_7)) (Submodule.instBotSubmodule.{u3, u3} S S (Ring.toSemiring.{u3} S _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_7)))) (Semiring.toModule.{u3} S (Ring.toSemiring.{u3} S _inst_7))))) -> (Basis.{u1, u4, u3} m R (Subtype.{succ u3} S (fun (x : S) => Membership.mem.{u3, u3} S (Ideal.{u3} S (Ring.toSemiring.{u3} S _inst_7)) (SetLike.instMembership.{u3, u3} (Ideal.{u3} S (Ring.toSemiring.{u3} S _inst_7)) S (Submodule.setLike.{u3, u3} S S (Ring.toSemiring.{u3} S _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_7)))) (Semiring.toModule.{u3} S (Ring.toSemiring.{u3} S _inst_7)))) x I)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Submodule.addCommMonoid.{u3, u3} S S (Ring.toSemiring.{u3} S _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_7)))) (Semiring.toModule.{u3} S (Ring.toSemiring.{u3} S _inst_7)) I) (Submodule.module'.{u4, u3, u3} R S S (Ring.toSemiring.{u3} S _inst_7) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_7)))) (Semiring.toModule.{u3} S (Ring.toSemiring.{u3} S _inst_7)) I (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_5)) (Algebra.toSMul.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_5) (Ring.toSemiring.{u3} S _inst_7) _inst_9) (Algebra.toModule.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_5) (Ring.toSemiring.{u3} S _inst_7) _inst_9) (IsScalarTower.right.{u4, u3} R S (CommRing.toCommSemiring.{u4} R _inst_5) (Ring.toSemiring.{u3} S _inst_7) _inst_9))) -> (Eq.{1} Nat (Fintype.card.{u1} m _inst_11) (Fintype.card.{u2} n _inst_10)))
 Case conversion may be inaccurate. Consider using '#align ideal.rank_eq Ideal.rank_eqₓ'. -/
 /-- If `S` a finite-dimensional ring extension of `R` which is free as an `R`-module,
 then the rank of an ideal `I` of `S` over `R` is the same as the rank of `S`.
@@ -1462,7 +1462,7 @@ end Fintype
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) ((fun (a : Type) (b : Type.{succ u2}) [self : HasLiftT.{1, succ (succ u2)} a b] => self.0) Nat Cardinal.{u2} (HasLiftT.mk.{1, succ (succ u2)} Nat Cardinal.{u2} (CoeTCₓ.coe.{1, succ (succ u2)} Nat Cardinal.{u2} (Nat.castCoe.{succ u2} Cardinal.{u2} Cardinal.hasNatCast.{u2}))) n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (finDimVectorspaceEquiv._proof_1.{u1} K _inst_1) (finDimVectorspaceEquiv._proof_2.{u1} K _inst_1) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.Function.module.{0, u1, u1} (Fin n) K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) (Nat.cast.{succ u2} Cardinal.{u2} Cardinal.instNatCastCardinal.{u2} n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13545 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1))))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) (Nat.cast.{succ u2} Cardinal.{u2} Cardinal.instNatCastCardinal.{u2} n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13545 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1))))
 Case conversion may be inaccurate. Consider using '#align fin_dim_vectorspace_equiv finDimVectorspaceEquivₓ'. -/
 -- TODO: merge with the `finrank` content
 /-- An `n`-dimensional `K`-vector space is equivalent to `fin n → K`. -/
@@ -1538,7 +1538,7 @@ theorem rank_quotient_add_rank (p : Submodule K V) :
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7), Eq.{succ (succ u2)} Cardinal.{u2} (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) V₁ (Submodule.setLike.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7)) (LinearMap.range.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) f)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) f)) (Submodule.module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) f))) (Module.rank.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)))) (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7), Eq.{succ (succ u2)} Cardinal.{u2} (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K (Subtype.{succ u2} V₁ (fun (x : V₁) => Membership.mem.{u2, u2} V₁ (Submodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) V₁ (Submodule.setLike.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7)) x (LinearMap.range.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) f))) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K 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(Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) f))) (Module.rank.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f))) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)))) (Module.rank.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)
+  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7), Eq.{succ (succ u2)} Cardinal.{u2} 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_inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) f))) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) f)) (Submodule.module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7 (LinearMap.range.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) f))) (Module.rank.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => 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(DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f))) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)))) (Module.rank.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)
 Case conversion may be inaccurate. Consider using '#align rank_range_add_rank_ker rank_range_add_rank_kerₓ'. -/
 /-- rank-nullity theorem -/
 theorem rank_range_add_rank_ker (f : V →ₗ[K] V₁) :
@@ -1552,7 +1552,7 @@ theorem rank_range_add_rank_ker (f : V →ₗ[K] V₁) :
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} V V₁ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) => V -> V₁) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Module.rank.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} V V₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => V₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Module.rank.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f))) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)))))
+  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} V V₁ (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => V₁) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Module.rank.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f))) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f)))))
 Case conversion may be inaccurate. Consider using '#align rank_eq_of_surjective rank_eq_of_surjectiveₓ'. -/
 theorem rank_eq_of_surjective (f : V →ₗ[K] V₁) (h : Surjective f) :
     Module.rank K V = Module.rank K V₁ + Module.rank K f.ker := by
@@ -1571,7 +1571,7 @@ open LinearMap
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} {V₂ : Type.{u2}} {V₃ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] [_inst_8 : AddCommGroup.{u2} V₂] [_inst_9 : Module.{u1, u2} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8)] [_inst_10 : AddCommGroup.{u2} V₃] [_inst_11 : Module.{u1, u2} K V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10)] (db : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (eb : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (cd : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (ce : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11), (LE.le.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Top.top.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _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 _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 _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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) db) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) eb))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (LinearMap.ker.{u1, u1, u2, u2, u2} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K 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(DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_3) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) db cd) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) eb ce)) -> (forall (d : V₂) (e : V₃), (Eq.{succ u2} V (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) => V₂ -> V) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) db d) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) => V₃ -> V) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) eb e)) -> (Exists.{succ u2} V₁ (fun (c : V₁) => And (Eq.{succ u2} V₂ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) cd c) d) (Eq.{succ u2} V₃ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11) => V₁ -> V₃) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₁ V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) ce c) e)))) -> (Eq.{succ (succ u2)} Cardinal.{u2} (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.rank.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7)) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_9) (Module.rank.{u1, u2} K V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_11)))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} {V₂ : Type.{u2}} {V₃ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] [_inst_8 : AddCommGroup.{u2} V₂] [_inst_9 : Module.{u1, u2} K V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8)] [_inst_10 : AddCommGroup.{u2} V₃] [_inst_11 : Module.{u1, u2} K V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10)] (db : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (eb : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (cd : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (ce : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11), (LE.le.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (Top.top.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Sup.sup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) db) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) eb))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (LinearMap.ker.{u1, u1, u2, u2, u2} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) cd) (Bot.bot.{u2} (Submodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Submodule.instBotSubmodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7))) -> (Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_3) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_9 _inst_3 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHomCompTriple.ids.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) db cd) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_11 _inst_3 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHomCompTriple.ids.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) eb ce)) -> (forall (d : V₂) (e : V₃), (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₂) => V) d) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) V₂ (fun (_x : V₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₂) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) db d) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) V₃ (fun (_x : V₃) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₃) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) eb e)) -> (Exists.{succ u2} V₁ (fun (c : V₁) => And (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₁) => V₂) c) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) cd c) d) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₁) => V₃) c) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₁) => V₃) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₁ V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) ce c) e)))) -> (Eq.{succ (succ u2)} Cardinal.{u2} (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.rank.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7)) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_9) (Module.rank.{u1, u2} K V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_11)))
+  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} {V₂ : Type.{u2}} {V₃ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] [_inst_8 : AddCommGroup.{u2} V₂] [_inst_9 : Module.{u1, u2} K V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8)] [_inst_10 : AddCommGroup.{u2} V₃] [_inst_11 : Module.{u1, u2} K V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10)] (db : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (eb : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (cd : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (ce : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11), (LE.le.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (Top.top.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Sup.sup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) db) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))) eb))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (LinearMap.ker.{u1, u1, u2, u2, u2} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) cd) (Bot.bot.{u2} (Submodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Submodule.instBotSubmodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7))) -> (Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_3) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHomCompTriple.ids.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) db cd) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) (RingHomCompTriple.ids.{u1, u1} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) eb ce)) -> (forall (d : V₂) (e : V₃), (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₂) => V) d) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) V₂ (fun (_x : V₂) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₂) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₂ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) db d) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) V₃ (fun (_x : V₃) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₃) => V) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) eb e)) -> (Exists.{succ u2} V₁ (fun (c : V₁) => And (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₁) => V₂) c) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₁) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₁ V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) cd c) d) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₁) => V₃) c) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V₁) => V₃) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} K K V₁ V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) ce c) e)))) -> (Eq.{succ (succ u2)} Cardinal.{u2} (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.rank.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7)) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_9) (Module.rank.{u1, u2} K V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_11)))
 Case conversion may be inaccurate. Consider using '#align rank_add_rank_split rank_add_rank_splitₓ'. -/
 /-- This is mostly an auxiliary lemma for `submodule.rank_sup_add_rank_inf_eq`. -/
 theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd : V₁ →ₗ[K] V₂)
@@ -1858,7 +1858,7 @@ theorem rank_le_domain (f : V →ₗ[K] V₁) : rank f ≤ Module.rank K V :=
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] [_inst_8 : Nontrivial.{u1} K], Eq.{succ (succ u3)} Cardinal.{u3} (LinearMap.rank.{u1, u2, u3} K V V' _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 (OfNat.ofNat.{max u2 u3} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) 0 (OfNat.mk.{max u2 u3} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) 0 (Zero.zero.{max u2 u3} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (LinearMap.hasZero.{u1, u1, u2, u3} K K V V' (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1)))))))) (OfNat.ofNat.{succ u3} Cardinal.{u3} 0 (OfNat.mk.{succ u3} Cardinal.{u3} 0 (Zero.zero.{succ u3} Cardinal.{u3} Cardinal.hasZero.{u3})))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] [_inst_8 : Nontrivial.{u1} K], Eq.{succ (succ u3)} Cardinal.{u3} (LinearMap.rank.{u1, u2, u3} K V V' _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 (OfNat.ofNat.{max u2 u3} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) 0 (Zero.toOfNat0.{max u2 u3} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (LinearMap.instZeroLinearMap.{u1, u1, u2, u3} K K V V' (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))))) (OfNat.ofNat.{succ u3} Cardinal.{u3} 0 (Zero.toOfNat0.{succ u3} Cardinal.{u3} Cardinal.instZeroCardinal.{u3}))
+  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] [_inst_8 : Nontrivial.{u1} K], Eq.{succ (succ u3)} Cardinal.{u3} (LinearMap.rank.{u1, u2, u3} K V V' _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 (OfNat.ofNat.{max u2 u3} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) 0 (Zero.toOfNat0.{max u2 u3} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (LinearMap.instZeroLinearMap.{u1, u1, u2, u3} K K V V' (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))))))) (OfNat.ofNat.{succ u3} Cardinal.{u3} 0 (Zero.toOfNat0.{succ u3} Cardinal.{u3} Cardinal.instZeroCardinal.{u3}))
 Case conversion may be inaccurate. Consider using '#align linear_map.rank_zero LinearMap.rank_zeroₓ'. -/
 @[simp]
 theorem rank_zero [Nontrivial K] : rank (0 : V →ₗ[K] V') = 0 := by
@@ -1887,7 +1887,7 @@ theorem lift_rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} {V'' : Type.{u4}} [_inst_1 : Ring.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] [_inst_8 : AddCommGroup.{u4} V''] [_inst_9 : Module.{u1, u4} K V'' (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V'' _inst_8)] (g : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (f : LinearMap.{u1, u1, u3, u4} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) V' V'' (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u4} V'' _inst_8) _inst_7 _inst_9), LE.le.{succ (max u4 u3)} Cardinal.{max u4 u3} Cardinal.hasLe.{max u4 u3} (Cardinal.lift.{u3, u4} (LinearMap.rank.{u1, u2, u4} K V V'' _inst_1 _inst_2 _inst_3 _inst_8 _inst_9 (LinearMap.comp.{u1, u1, u1, u2, u3, u4} K K K V V' V'' (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u4} V'' _inst_8) _inst_3 _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) f g))) (LinearOrder.min.{succ (max u4 u3)} Cardinal.{max u4 u3} Cardinal.linearOrder.{max u4 u3} (Cardinal.lift.{u3, u4} (LinearMap.rank.{u1, u3, u4} K V' V'' _inst_1 _inst_6 _inst_7 _inst_8 _inst_9 f)) (Cardinal.lift.{u4, u3} (LinearMap.rank.{u1, u2, u3} K V V' _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 g)))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} {V'' : Type.{u4}} [_inst_1 : Ring.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] [_inst_8 : AddCommGroup.{u4} V''] [_inst_9 : Module.{u1, u4} K V'' (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V'' _inst_8)] (g : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (f : LinearMap.{u1, u1, u3, u4} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) V' V'' (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u4} V'' _inst_8) _inst_7 _inst_9), LE.le.{max (succ u3) (succ u4)} Cardinal.{max u4 u3} Cardinal.instLECardinal.{max u3 u4} (Cardinal.lift.{u3, u4} (LinearMap.rank.{u1, u2, u4} K V V'' _inst_1 _inst_2 _inst_3 _inst_8 _inst_9 (LinearMap.comp.{u1, u1, u1, u2, u3, u4} K K K V V' V'' (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u4} V'' _inst_8) _inst_3 _inst_7 _inst_9 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHomCompTriple.ids.{u1, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) f g))) (Min.min.{max (succ u3) (succ u4)} Cardinal.{max u4 u3} (CanonicallyLinearOrderedAddMonoid.toMin.{max (succ u3) (succ u4)} Cardinal.{max u4 u3} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{max u3 u4}) (Cardinal.lift.{u3, u4} (LinearMap.rank.{u1, u3, u4} K V' V'' _inst_1 _inst_6 _inst_7 _inst_8 _inst_9 f)) (Cardinal.lift.{u4, u3} (LinearMap.rank.{u1, u2, u3} K V V' _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 g)))
+  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} {V'' : Type.{u4}} [_inst_1 : Ring.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] [_inst_8 : AddCommGroup.{u4} V''] [_inst_9 : Module.{u1, u4} K V'' (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V'' _inst_8)] (g : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (f : LinearMap.{u1, u1, u3, u4} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) V' V'' (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u4} V'' _inst_8) _inst_7 _inst_9), LE.le.{max (succ u3) (succ u4)} Cardinal.{max u4 u3} Cardinal.instLECardinal.{max u3 u4} (Cardinal.lift.{u3, u4} (LinearMap.rank.{u1, u2, u4} K V V'' _inst_1 _inst_2 _inst_3 _inst_8 _inst_9 (LinearMap.comp.{u1, u1, u1, u2, u3, u4} K K K V V' V'' (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u4} V'' _inst_8) _inst_3 _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomCompTriple.ids.{u1, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) f g))) (Min.min.{max (succ u3) (succ u4)} Cardinal.{max u4 u3} (CanonicallyLinearOrderedAddMonoid.toMin.{max (succ u3) (succ u4)} Cardinal.{max u4 u3} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{max u3 u4}) (Cardinal.lift.{u3, u4} (LinearMap.rank.{u1, u3, u4} K V' V'' _inst_1 _inst_6 _inst_7 _inst_8 _inst_9 f)) (Cardinal.lift.{u4, u3} (LinearMap.rank.{u1, u2, u3} K V V' _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 g)))
 Case conversion may be inaccurate. Consider using '#align linear_map.lift_rank_comp_le LinearMap.lift_rank_comp_leₓ'. -/
 /-- The rank of the composition of two maps is less than the minimum of their ranks. -/
 theorem lift_rank_comp_le (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
@@ -1908,7 +1908,7 @@ theorem rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) : rank
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} {V'₁ : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] [_inst_10 : AddCommGroup.{u3} V'₁] [_inst_11 : Module.{u1, u3} K V'₁ (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V'₁ _inst_10)] (g : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (f : LinearMap.{u1, u1, u3, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) V' V'₁ (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u3} V'₁ _inst_10) _inst_7 _inst_11), LE.le.{succ u3} Cardinal.{u3} Cardinal.hasLe.{u3} (LinearMap.rank.{u1, u2, u3} K V V'₁ _inst_1 _inst_2 _inst_3 _inst_10 _inst_11 (LinearMap.comp.{u1, u1, u1, u2, u3, u3} K K K V V' V'₁ (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u3} V'₁ _inst_10) _inst_3 _inst_7 _inst_11 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) f g)) (LinearOrder.min.{succ u3} Cardinal.{u3} Cardinal.linearOrder.{u3} (LinearMap.rank.{u1, u3, u3} K V' V'₁ _inst_1 _inst_6 _inst_7 _inst_10 _inst_11 f) (LinearMap.rank.{u1, u2, u3} K V V' _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 g))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} {V'₁ : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] [_inst_10 : AddCommGroup.{u3} V'₁] [_inst_11 : Module.{u1, u3} K V'₁ (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V'₁ _inst_10)] (g : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (f : LinearMap.{u1, u1, u3, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) V' V'₁ (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u3} V'₁ _inst_10) _inst_7 _inst_11), LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} (LinearMap.rank.{u1, u2, u3} K V V'₁ _inst_1 _inst_2 _inst_3 _inst_10 _inst_11 (LinearMap.comp.{u1, u1, u1, u2, u3, u3} K K K V V' V'₁ (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u3} V'₁ _inst_10) _inst_3 _inst_7 _inst_11 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHomCompTriple.ids.{u1, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) f g)) (Min.min.{succ u3} Cardinal.{u3} (CanonicallyLinearOrderedAddMonoid.toMin.{succ u3} Cardinal.{u3} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u3}) (LinearMap.rank.{u1, u3, u3} K V' V'₁ _inst_1 _inst_6 _inst_7 _inst_10 _inst_11 f) (LinearMap.rank.{u1, u2, u3} K V V' _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 g))
+  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} {V'₁ : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] [_inst_10 : AddCommGroup.{u3} V'₁] [_inst_11 : Module.{u1, u3} K V'₁ (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V'₁ _inst_10)] (g : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (f : LinearMap.{u1, u1, u3, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) V' V'₁ (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u3} V'₁ _inst_10) _inst_7 _inst_11), LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} (LinearMap.rank.{u1, u2, u3} K V V'₁ _inst_1 _inst_2 _inst_3 _inst_10 _inst_11 (LinearMap.comp.{u1, u1, u1, u2, u3, u3} K K K V V' V'₁ (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u3} V'₁ _inst_10) _inst_3 _inst_7 _inst_11 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomCompTriple.ids.{u1, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) f g)) (Min.min.{succ u3} Cardinal.{u3} (CanonicallyLinearOrderedAddMonoid.toMin.{succ u3} Cardinal.{u3} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u3}) (LinearMap.rank.{u1, u3, u3} K V' V'₁ _inst_1 _inst_6 _inst_7 _inst_10 _inst_11 f) (LinearMap.rank.{u1, u2, u3} K V V' _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 g))
 Case conversion may be inaccurate. Consider using '#align linear_map.rank_comp_le LinearMap.rank_comp_leₓ'. -/
 /-- The rank of the composition of two maps is less than the minimum of their ranks.
 
@@ -1930,7 +1930,7 @@ variable [AddCommGroup V'] [Module K V']
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] (f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (g : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7), LE.le.{succ u3} Cardinal.{u3} Cardinal.hasLe.{u3} (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (instHAdd.{max u2 u3} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (LinearMap.hasAdd.{u1, u1, u2, u3} K K V V' (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))))) f g)) (HAdd.hAdd.{succ u3, succ u3, succ u3} Cardinal.{u3} Cardinal.{u3} Cardinal.{u3} (instHAdd.{succ u3} Cardinal.{u3} Cardinal.hasAdd.{u3}) (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f) (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 g))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] (f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (g : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7), LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (instHAdd.{max u2 u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (LinearMap.instAddLinearMap.{u1, u1, u2, u3} K K V V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))))) f g)) (HAdd.hAdd.{succ u3, succ u3, succ u3} Cardinal.{u3} Cardinal.{u3} Cardinal.{u3} (instHAdd.{succ u3} Cardinal.{u3} Cardinal.instAddCardinal.{u3}) (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f) (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 g))
+  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] (f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (g : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7), LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 (HAdd.hAdd.{max u2 u3, max u2 u3, max u2 u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (instHAdd.{max u2 u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (LinearMap.instAddLinearMap.{u1, u1, u2, u3} K K V V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))))) f g)) (HAdd.hAdd.{succ u3, succ u3, succ u3} Cardinal.{u3} Cardinal.{u3} Cardinal.{u3} (instHAdd.{succ u3} Cardinal.{u3} Cardinal.instAddCardinal.{u3}) (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f) (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 g))
 Case conversion may be inaccurate. Consider using '#align linear_map.rank_add_le LinearMap.rank_add_leₓ'. -/
 theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
   calc
@@ -1950,7 +1950,7 @@ theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {η : Type.{u4}} (s : Finset.{u4} η) (f : η -> (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7)), LE.le.{succ u3} Cardinal.{u3} Cardinal.hasLe.{u3} (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 (Finset.sum.{max u2 u3, u4} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) η (LinearMap.addCommMonoid.{u1, u1, u2, u3} K K V V' (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) s (fun (d : η) => f d))) (Finset.sum.{succ u3, u4} Cardinal.{u3} η (OrderedAddCommMonoid.toAddCommMonoid.{succ u3} Cardinal.{u3} (OrderedSemiring.toOrderedAddCommMonoid.{succ u3} Cardinal.{u3} (OrderedCommSemiring.toOrderedSemiring.{succ u3} Cardinal.{u3} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u3} Cardinal.{u3} Cardinal.canonicallyOrderedCommSemiring.{u3})))) s (fun (d : η) => LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 (f d)))
 but is expected to have type
-  forall {K : Type.{u2}} {V : Type.{u3}} {V' : Type.{u4}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} K V (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_6 : AddCommGroup.{u4} V'] [_inst_7 : Module.{u2, u4} K V' (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u4} V' _inst_6)] {η : Type.{u1}} (s : Finset.{u1} η) (f : η -> (LinearMap.{u2, u2, u3, u4} K K (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_1)) (RingHom.id.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V' _inst_6) _inst_3 _inst_7)), LE.le.{succ u4} Cardinal.{u4} Cardinal.instLECardinal.{u4} (LinearMap.rank.{u2, u3, u4} K V V' (DivisionRing.toRing.{u2} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 (Finset.sum.{max u4 u3, u1} (LinearMap.{u2, u2, u3, u4} K K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (RingHom.id.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V' _inst_6) _inst_3 _inst_7) η (LinearMap.addCommMonoid.{u2, u2, u3, u4} K K V V' (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u2} K (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K _inst_1))))) s (fun (d : η) => f d))) (Finset.sum.{succ u4, u1} Cardinal.{u4} η (OrderedAddCommMonoid.toAddCommMonoid.{succ u4} Cardinal.{u4} (OrderedSemiring.toOrderedAddCommMonoid.{succ u4} Cardinal.{u4} (OrderedCommSemiring.toOrderedSemiring.{succ u4} Cardinal.{u4} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u4} Cardinal.{u4} Cardinal.canonicallyOrderedCommSemiring.{u4})))) s (fun (d : η) => LinearMap.rank.{u2, u3, u4} K V V' (DivisionRing.toRing.{u2} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 (f d)))
+  forall {K : Type.{u2}} {V : Type.{u3}} {V' : Type.{u4}} [_inst_1 : DivisionRing.{u2} K] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} K V (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_6 : AddCommGroup.{u4} V'] [_inst_7 : Module.{u2, u4} K V' (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u4} V' _inst_6)] {η : Type.{u1}} (s : Finset.{u1} η) (f : η -> (LinearMap.{u2, u2, u3, u4} K K (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_1)) (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_1)) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V' _inst_6) _inst_3 _inst_7)), LE.le.{succ u4} Cardinal.{u4} Cardinal.instLECardinal.{u4} (LinearMap.rank.{u2, u3, u4} K V V' (DivisionRing.toRing.{u2} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 (Finset.sum.{max u4 u3, u1} (LinearMap.{u2, u2, u3, u4} K K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V' _inst_6) _inst_3 _inst_7) η (LinearMap.addCommMonoid.{u2, u2, u3, u4} K K V V' (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K _inst_1))))) s (fun (d : η) => f d))) (Finset.sum.{succ u4, u1} Cardinal.{u4} η (OrderedAddCommMonoid.toAddCommMonoid.{succ u4} Cardinal.{u4} (OrderedSemiring.toOrderedAddCommMonoid.{succ u4} Cardinal.{u4} (OrderedCommSemiring.toOrderedSemiring.{succ u4} Cardinal.{u4} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u4} Cardinal.{u4} Cardinal.canonicallyOrderedCommSemiring.{u4})))) s (fun (d : η) => LinearMap.rank.{u2, u3, u4} K V V' (DivisionRing.toRing.{u2} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 (f d)))
 Case conversion may be inaccurate. Consider using '#align linear_map.rank_finset_sum_le LinearMap.rank_finset_sum_leₓ'. -/
 theorem rank_finset_sum_le {η} (s : Finset η) (f : η → V →ₗ[K] V') :
     rank (∑ d in s, f d) ≤ ∑ d in s, rank (f d) :=
@@ -1962,7 +1962,7 @@ theorem rank_finset_sum_le {η} (s : Finset η) (f : η → V →ₗ[K] V') :
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {c : Cardinal.{u3}} {f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.hasLe.{u3} c (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Set.{u2} V) (fun (s : Set.{u2} V) => And (Eq.{succ (succ (max u2 u3))} Cardinal.{max u2 u3} (Cardinal.lift.{u3, u2} (Cardinal.mk.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s))) (Cardinal.lift.{u2, u3} c)) (LinearIndependent.{u2, u1, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s) K V' (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s) => coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) => V -> V') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} K K V V' (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s) V (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s) V (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s) V (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) s) V (coeSubtype.{succ u2} V (fun (x : V) => Membership.Mem.{u2, u2} V (Set.{u2} V) (Set.hasMem.{u2} V) x s))))) x)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {c : Cardinal.{u3}} {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} c (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Set.{u2} V) (fun (s : Set.{u2} V) => And (Eq.{max (succ (succ u2)) (succ (succ u3))} Cardinal.{max u2 u3} (Cardinal.lift.{u3, u2} (Cardinal.mk.{u2} (Set.Elem.{u2} V s))) (Cardinal.lift.{u2, u3} c)) (LinearIndependent.{u2, u1, u3} (Set.Elem.{u2} V s) K V' (fun (x : Set.Elem.{u2} V s) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => V') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s) x)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
+  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {c : Cardinal.{u3}} {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} c (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Set.{u2} V) (fun (s : Set.{u2} V) => And (Eq.{max (succ (succ u2)) (succ (succ u3))} Cardinal.{max u2 u3} (Cardinal.lift.{u3, u2} (Cardinal.mk.{u2} (Set.Elem.{u2} V s))) (Cardinal.lift.{u2, u3} c)) (LinearIndependent.{u2, u1, u3} (Set.Elem.{u2} V s) K V' (fun (x : Set.Elem.{u2} V s) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => V') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x s) x)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
 Case conversion may be inaccurate. Consider using '#align linear_map.le_rank_iff_exists_linear_independent LinearMap.le_rank_iff_exists_linearIndependentₓ'. -/
 theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'} :
     c ≤ rank f ↔
@@ -1992,7 +1992,7 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'}
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {n : Nat} {f : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.hasLe.{u3} ((fun (a : Type) (b : Type.{succ u3}) [self : HasLiftT.{1, succ (succ u3)} a b] => self.0) Nat Cardinal.{u3} (HasLiftT.mk.{1, succ (succ u3)} Nat Cardinal.{u3} (CoeTCₓ.coe.{1, succ (succ u3)} Nat Cardinal.{u3} (Nat.castCoe.{succ u3} Cardinal.{u3} Cardinal.hasNatCast.{u3}))) n) (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Finset.{u2} V) (fun (s : Finset.{u2} V) => And (Eq.{1} Nat (Finset.card.{u2} V s) n) (LinearIndependent.{u2, u1, u3} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)) K V' (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)) => coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (fun (_x : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) => V -> V') (LinearMap.hasCoeToFun.{u1, u1, u2, u3} K K V V' (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)) V (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)) V (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)) V (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} V) Type.{u2} (Set.hasCoeToSort.{u2} V) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)) V (coeSubtype.{succ u2} V (fun (x : V) => Membership.Mem.{u2, u2} V (Set.{u2} V) (Set.hasMem.{u2} V) x ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} V) (Set.{u2} V) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} V) (Set.{u2} V) (Finset.Set.hasCoeT.{u2} V))) s)))))) x)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {n : Nat} {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} (Nat.cast.{succ u3} Cardinal.{u3} Cardinal.instNatCastCardinal.{u3} n) (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Finset.{u2} V) (fun (s : Finset.{u2} V) => And (Eq.{1} Nat (Finset.card.{u2} V s) n) (LinearIndependent.{u2, u1, u3} (Set.Elem.{u2} V (Finset.toSet.{u2} V s)) K V' (fun (x : Set.Elem.{u2} V (Finset.toSet.{u2} V s)) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => V') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x (Finset.toSet.{u2} V s)) x)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
+  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {n : Nat} {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} (Nat.cast.{succ u3} Cardinal.{u3} Cardinal.instNatCastCardinal.{u3} n) (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Finset.{u2} V) (fun (s : Finset.{u2} V) => And (Eq.{1} Nat (Finset.card.{u2} V s) n) (LinearIndependent.{u2, u1, u3} (Set.Elem.{u2} V (Finset.toSet.{u2} V s)) K V' (fun (x : Set.Elem.{u2} V (Finset.toSet.{u2} V s)) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => V') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1))))) f (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x (Finset.toSet.{u2} V s)) x)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
 Case conversion may be inaccurate. Consider using '#align linear_map.le_rank_iff_exists_linear_independent_finset LinearMap.le_rank_iff_exists_linearIndependent_finsetₓ'. -/
 theorem le_rank_iff_exists_linearIndependent_finset {n : ℕ} {f : V →ₗ[K] V'} :
     ↑n ≤ rank f ↔ ∃ s : Finset V, s.card = n ∧ LinearIndependent K fun x : (s : Set V) => f x :=

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

@@ -1418,7 +1418,7 @@ variable [Fintype η]
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] {V : Type.{u1}} {η : Type.{u1}} [_inst_16 : Fintype.{u1} η] [_inst_17 : AddCommGroup.{u1} V] [_inst_18 : Module.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17)] [_inst_19 : Module.Free.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u1, u1} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17)) (Pi.Function.module.{u1, u1, u1} η K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18)) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) (Fintype.card.{u1} η _inst_16)) (Module.rank.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] {V : Type.{u1}} {η : Type.{u1}} [_inst_16 : Fintype.{u1} η] [_inst_17 : AddCommGroup.{u1} V] [_inst_18 : Module.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17)] [_inst_19 : Module.Free.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u1, u1} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17)) (Pi.module.{u1, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.12992 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17) (fun (i : η) => _inst_18))) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} (Fintype.card.{u1} η _inst_16)) (Module.rank.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18))
+  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] {V : Type.{u1}} {η : Type.{u1}} [_inst_16 : Fintype.{u1} η] [_inst_17 : AddCommGroup.{u1} V] [_inst_18 : Module.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17)] [_inst_19 : Module.Free.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u1, u1} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17)) (Pi.module.{u1, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13034 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17) (fun (i : η) => _inst_18))) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} (Fintype.card.{u1} η _inst_16)) (Module.rank.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18))
 Case conversion may be inaccurate. Consider using '#align rank_fun rank_funₓ'. -/
 theorem rank_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] [Module.Free K V] :
     Module.rank K (η → V) = Fintype.card η * Module.rank K V := by
@@ -1429,7 +1429,7 @@ theorem rank_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] [Mod
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {η : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] [_inst_15 : Fintype.{u3} η], Eq.{succ (succ (max u3 u2))} Cardinal.{max u3 u2} (Module.rank.{u1, max u3 u2} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u3, u2} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3)) (Pi.Function.module.{u3, u1, u2} η K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)) (HMul.hMul.{succ (max u3 u2), succ (max u3 u2), succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.{max u3 u2} Cardinal.{max u3 u2} (instHMul.{succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.hasMul.{max u3 u2}) ((fun (a : Type) (b : Type.{succ (max u3 u2)}) [self : HasLiftT.{1, succ (succ (max u3 u2))} a b] => self.0) Nat Cardinal.{max u3 u2} (HasLiftT.mk.{1, succ (succ (max u3 u2))} Nat Cardinal.{max u3 u2} (CoeTCₓ.coe.{1, succ (succ (max u3 u2))} Nat Cardinal.{max u3 u2} (Nat.castCoe.{succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.hasNatCast.{max u3 u2}))) (Fintype.card.{u3} η _inst_15)) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {η : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] [_inst_15 : Fintype.{u3} η], Eq.{max (succ (succ u3)) (succ (succ u2))} Cardinal.{max u3 u2} (Module.rank.{u1, max u3 u2} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u3, u2} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3)) (Pi.module.{u3, u2, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13126 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (fun (i : η) => _inst_4))) (HMul.hMul.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.{max u2 u3} Cardinal.{max u3 u2} (instHMul.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instMulCardinal.{max u3 u2}) (Nat.cast.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instNatCastCardinal.{max u3 u2} (Fintype.card.{u3} η _inst_15)) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)))
+  forall {K : Type.{u1}} {V : Type.{u2}} {η : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] [_inst_15 : Fintype.{u3} η], Eq.{max (succ (succ u3)) (succ (succ u2))} Cardinal.{max u3 u2} (Module.rank.{u1, max u3 u2} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u3, u2} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3)) (Pi.module.{u3, u2, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13168 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (fun (i : η) => _inst_4))) (HMul.hMul.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.{max u2 u3} Cardinal.{max u3 u2} (instHMul.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instMulCardinal.{max u3 u2}) (Nat.cast.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instNatCastCardinal.{max u3 u2} (Fintype.card.{u3} η _inst_15)) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)))
 Case conversion may be inaccurate. Consider using '#align rank_fun_eq_lift_mul rank_fun_eq_lift_mulₓ'. -/
 theorem rank_fun_eq_lift_mul :
     Module.rank K (η → V) =
@@ -1441,7 +1441,7 @@ theorem rank_fun_eq_lift_mul :
 lean 3 declaration is
   forall {K : Type.{u1}} {η : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_15 : Fintype.{u2} η], Eq.{succ (succ (max u2 u1))} Cardinal.{max u2 u1} (Module.rank.{u1, max u2 u1} K (η -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => K) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.Function.module.{u2, u1, u1} η K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) ((fun (a : Type) (b : Type.{succ (max u2 u1)}) [self : HasLiftT.{1, succ (succ (max u2 u1))} a b] => self.0) Nat Cardinal.{max u2 u1} (HasLiftT.mk.{1, succ (succ (max u2 u1))} Nat Cardinal.{max u2 u1} (CoeTCₓ.coe.{1, succ (succ (max u2 u1))} Nat Cardinal.{max u2 u1} (Nat.castCoe.{succ (max u2 u1)} Cardinal.{max u2 u1} Cardinal.hasNatCast.{max u2 u1}))) (Fintype.card.{u2} η _inst_15))
 but is expected to have type
-  forall {K : Type.{u1}} {η : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_15 : Fintype.{u2} η], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (η -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => K) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{u2, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13273 : η) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : η) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1))) (Nat.cast.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instNatCastCardinal.{max u1 u2} (Fintype.card.{u2} η _inst_15))
+  forall {K : Type.{u1}} {η : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_15 : Fintype.{u2} η], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (η -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => K) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{u2, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13315 : η) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : η) => Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) (Nat.cast.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instNatCastCardinal.{max u1 u2} (Fintype.card.{u2} η _inst_15))
 Case conversion may be inaccurate. Consider using '#align rank_fun' rank_fun'ₓ'. -/
 theorem rank_fun' : Module.rank K (η → K) = Fintype.card η := by
   rw [rank_fun_eq_lift_mul, rank_self, Cardinal.lift_one, mul_one, Cardinal.natCast_inj]
@@ -1451,7 +1451,7 @@ theorem rank_fun' : Module.rank K (η → K) = Fintype.card η := by
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K ((Fin n) -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.Function.module.{0, u1, u1} (Fin n) K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K ((Fin n) -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13409 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1))) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)
+  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K ((Fin n) -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13456 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)
 Case conversion may be inaccurate. Consider using '#align rank_fin_fun rank_fin_funₓ'. -/
 theorem rank_fin_fun (n : ℕ) : Module.rank K (Fin n → K) = n := by simp [rank_fun']
 #align rank_fin_fun rank_fin_fun
@@ -1462,7 +1462,7 @@ end Fintype
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) ((fun (a : Type) (b : Type.{succ u2}) [self : HasLiftT.{1, succ (succ u2)} a b] => self.0) Nat Cardinal.{u2} (HasLiftT.mk.{1, succ (succ u2)} Nat Cardinal.{u2} (CoeTCₓ.coe.{1, succ (succ u2)} Nat Cardinal.{u2} (Nat.castCoe.{succ u2} Cardinal.{u2} Cardinal.hasNatCast.{u2}))) n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (finDimVectorspaceEquiv._proof_1.{u1} K _inst_1) (finDimVectorspaceEquiv._proof_2.{u1} K _inst_1) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.Function.module.{0, u1, u1} (Fin n) K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) (Nat.cast.{succ u2} Cardinal.{u2} Cardinal.instNatCastCardinal.{u2} n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13497 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1)))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) (Nat.cast.{succ u2} Cardinal.{u2} Cardinal.instNatCastCardinal.{u2} n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13545 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1))))
 Case conversion may be inaccurate. Consider using '#align fin_dim_vectorspace_equiv finDimVectorspaceEquivₓ'. -/
 -- TODO: merge with the `finrank` content
 /-- An `n`-dimensional `K`-vector space is equivalent to `fin n → K`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

@@ -1418,7 +1418,7 @@ variable [Fintype η]
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] {V : Type.{u1}} {η : Type.{u1}} [_inst_16 : Fintype.{u1} η] [_inst_17 : AddCommGroup.{u1} V] [_inst_18 : Module.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17)] [_inst_19 : Module.Free.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u1, u1} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17)) (Pi.Function.module.{u1, u1, u1} η K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18)) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) (Fintype.card.{u1} η _inst_16)) (Module.rank.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] {V : Type.{u1}} {η : Type.{u1}} [_inst_16 : Fintype.{u1} η] [_inst_17 : AddCommGroup.{u1} V] [_inst_18 : Module.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17)] [_inst_19 : Module.Free.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u1, u1} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17)) (Pi.module.{u1, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.12958 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17) (fun (i : η) => _inst_18))) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} (Fintype.card.{u1} η _inst_16)) (Module.rank.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18))
+  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] {V : Type.{u1}} {η : Type.{u1}} [_inst_16 : Fintype.{u1} η] [_inst_17 : AddCommGroup.{u1} V] [_inst_18 : Module.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17)] [_inst_19 : Module.Free.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u1, u1} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17)) (Pi.module.{u1, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.12992 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17) (fun (i : η) => _inst_18))) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} (Fintype.card.{u1} η _inst_16)) (Module.rank.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18))
 Case conversion may be inaccurate. Consider using '#align rank_fun rank_funₓ'. -/
 theorem rank_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] [Module.Free K V] :
     Module.rank K (η → V) = Fintype.card η * Module.rank K V := by
@@ -1429,7 +1429,7 @@ theorem rank_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] [Mod
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {η : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] [_inst_15 : Fintype.{u3} η], Eq.{succ (succ (max u3 u2))} Cardinal.{max u3 u2} (Module.rank.{u1, max u3 u2} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u3, u2} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3)) (Pi.Function.module.{u3, u1, u2} η K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)) (HMul.hMul.{succ (max u3 u2), succ (max u3 u2), succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.{max u3 u2} Cardinal.{max u3 u2} (instHMul.{succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.hasMul.{max u3 u2}) ((fun (a : Type) (b : Type.{succ (max u3 u2)}) [self : HasLiftT.{1, succ (succ (max u3 u2))} a b] => self.0) Nat Cardinal.{max u3 u2} (HasLiftT.mk.{1, succ (succ (max u3 u2))} Nat Cardinal.{max u3 u2} (CoeTCₓ.coe.{1, succ (succ (max u3 u2))} Nat Cardinal.{max u3 u2} (Nat.castCoe.{succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.hasNatCast.{max u3 u2}))) (Fintype.card.{u3} η _inst_15)) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {η : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] [_inst_15 : Fintype.{u3} η], Eq.{max (succ (succ u3)) (succ (succ u2))} Cardinal.{max u3 u2} (Module.rank.{u1, max u3 u2} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u3, u2} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3)) (Pi.module.{u3, u2, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13092 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (fun (i : η) => _inst_4))) (HMul.hMul.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.{max u2 u3} Cardinal.{max u3 u2} (instHMul.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instMulCardinal.{max u3 u2}) (Nat.cast.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instNatCastCardinal.{max u3 u2} (Fintype.card.{u3} η _inst_15)) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)))
+  forall {K : Type.{u1}} {V : Type.{u2}} {η : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] [_inst_15 : Fintype.{u3} η], Eq.{max (succ (succ u3)) (succ (succ u2))} Cardinal.{max u3 u2} (Module.rank.{u1, max u3 u2} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u3, u2} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3)) (Pi.module.{u3, u2, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13126 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (fun (i : η) => _inst_4))) (HMul.hMul.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.{max u2 u3} Cardinal.{max u3 u2} (instHMul.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instMulCardinal.{max u3 u2}) (Nat.cast.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instNatCastCardinal.{max u3 u2} (Fintype.card.{u3} η _inst_15)) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)))
 Case conversion may be inaccurate. Consider using '#align rank_fun_eq_lift_mul rank_fun_eq_lift_mulₓ'. -/
 theorem rank_fun_eq_lift_mul :
     Module.rank K (η → V) =
@@ -1441,7 +1441,7 @@ theorem rank_fun_eq_lift_mul :
 lean 3 declaration is
   forall {K : Type.{u1}} {η : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_15 : Fintype.{u2} η], Eq.{succ (succ (max u2 u1))} Cardinal.{max u2 u1} (Module.rank.{u1, max u2 u1} K (η -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => K) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.Function.module.{u2, u1, u1} η K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) ((fun (a : Type) (b : Type.{succ (max u2 u1)}) [self : HasLiftT.{1, succ (succ (max u2 u1))} a b] => self.0) Nat Cardinal.{max u2 u1} (HasLiftT.mk.{1, succ (succ (max u2 u1))} Nat Cardinal.{max u2 u1} (CoeTCₓ.coe.{1, succ (succ (max u2 u1))} Nat Cardinal.{max u2 u1} (Nat.castCoe.{succ (max u2 u1)} Cardinal.{max u2 u1} Cardinal.hasNatCast.{max u2 u1}))) (Fintype.card.{u2} η _inst_15))
 but is expected to have type
-  forall {K : Type.{u1}} {η : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_15 : Fintype.{u2} η], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (η -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => K) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{u2, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13239 : η) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : η) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1))) (Nat.cast.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instNatCastCardinal.{max u1 u2} (Fintype.card.{u2} η _inst_15))
+  forall {K : Type.{u1}} {η : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_15 : Fintype.{u2} η], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (η -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => K) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{u2, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13273 : η) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : η) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1))) (Nat.cast.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instNatCastCardinal.{max u1 u2} (Fintype.card.{u2} η _inst_15))
 Case conversion may be inaccurate. Consider using '#align rank_fun' rank_fun'ₓ'. -/
 theorem rank_fun' : Module.rank K (η → K) = Fintype.card η := by
   rw [rank_fun_eq_lift_mul, rank_self, Cardinal.lift_one, mul_one, Cardinal.natCast_inj]
@@ -1451,7 +1451,7 @@ theorem rank_fun' : Module.rank K (η → K) = Fintype.card η := by
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K ((Fin n) -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.Function.module.{0, u1, u1} (Fin n) K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K ((Fin n) -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13375 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1))) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)
+  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K ((Fin n) -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13409 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1))) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)
 Case conversion may be inaccurate. Consider using '#align rank_fin_fun rank_fin_funₓ'. -/
 theorem rank_fin_fun (n : ℕ) : Module.rank K (Fin n → K) = n := by simp [rank_fun']
 #align rank_fin_fun rank_fin_fun
@@ -1462,7 +1462,7 @@ end Fintype
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) ((fun (a : Type) (b : Type.{succ u2}) [self : HasLiftT.{1, succ (succ u2)} a b] => self.0) Nat Cardinal.{u2} (HasLiftT.mk.{1, succ (succ u2)} Nat Cardinal.{u2} (CoeTCₓ.coe.{1, succ (succ u2)} Nat Cardinal.{u2} (Nat.castCoe.{succ u2} Cardinal.{u2} Cardinal.hasNatCast.{u2}))) n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (finDimVectorspaceEquiv._proof_1.{u1} K _inst_1) (finDimVectorspaceEquiv._proof_2.{u1} K _inst_1) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.Function.module.{0, u1, u1} (Fin n) K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) (Nat.cast.{succ u2} Cardinal.{u2} Cardinal.instNatCastCardinal.{u2} n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13463 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1)))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) (Nat.cast.{succ u2} Cardinal.{u2} Cardinal.instNatCastCardinal.{u2} n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13497 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1)))
 Case conversion may be inaccurate. Consider using '#align fin_dim_vectorspace_equiv finDimVectorspaceEquivₓ'. -/
 -- TODO: merge with the `finrank` content
 /-- An `n`-dimensional `K`-vector space is equivalent to `fin n → K`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/17ad94b4953419f3e3ce3e77da3239c62d1d09f0

@@ -1267,7 +1267,7 @@ variable (R)
 #print rank_self /-
 @[simp]
 theorem rank_self : Module.rank R R = 1 := by
-  rw [← Cardinal.lift_inj, ← (Basis.singleton PUnit R).mk_eq_rank, Cardinal.mk_pUnit]
+  rw [← Cardinal.lift_inj, ← (Basis.singleton PUnit R).mk_eq_rank, Cardinal.mk_punit]
 #align rank_self rank_self
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/17ad94b4953419f3e3ce3e77da3239c62d1d09f0

@@ -1876,11 +1876,19 @@ theorem rank_comp_le_left (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') : rank (f.
 #align linear_map.rank_comp_le_left LinearMap.rank_comp_le_left
 -/
 
+#print LinearMap.lift_rank_comp_le_right /-
 theorem lift_rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
     Cardinal.lift.{v'} (rank (f.comp g)) ≤ Cardinal.lift.{v''} (rank g) := by
   rw [rank, rank, LinearMap.range_comp] <;> exact lift_rank_map_le _ _
 #align linear_map.lift_rank_comp_le_right LinearMap.lift_rank_comp_le_right
+-/
 
+/- warning: linear_map.lift_rank_comp_le -> LinearMap.lift_rank_comp_le is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} {V'' : Type.{u4}} [_inst_1 : Ring.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] [_inst_8 : AddCommGroup.{u4} V''] [_inst_9 : Module.{u1, u4} K V'' (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V'' _inst_8)] (g : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (f : LinearMap.{u1, u1, u3, u4} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) V' V'' (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u4} V'' _inst_8) _inst_7 _inst_9), LE.le.{succ (max u4 u3)} Cardinal.{max u4 u3} Cardinal.hasLe.{max u4 u3} (Cardinal.lift.{u3, u4} (LinearMap.rank.{u1, u2, u4} K V V'' _inst_1 _inst_2 _inst_3 _inst_8 _inst_9 (LinearMap.comp.{u1, u1, u1, u2, u3, u4} K K K V V' V'' (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u4} V'' _inst_8) _inst_3 _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) f g))) (LinearOrder.min.{succ (max u4 u3)} Cardinal.{max u4 u3} Cardinal.linearOrder.{max u4 u3} (Cardinal.lift.{u3, u4} (LinearMap.rank.{u1, u3, u4} K V' V'' _inst_1 _inst_6 _inst_7 _inst_8 _inst_9 f)) (Cardinal.lift.{u4, u3} (LinearMap.rank.{u1, u2, u3} K V V' _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 g)))
+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} {V'' : Type.{u4}} [_inst_1 : Ring.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] [_inst_8 : AddCommGroup.{u4} V''] [_inst_9 : Module.{u1, u4} K V'' (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V'' _inst_8)] (g : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (f : LinearMap.{u1, u1, u3, u4} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) V' V'' (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u4} V'' _inst_8) _inst_7 _inst_9), LE.le.{max (succ u3) (succ u4)} Cardinal.{max u4 u3} Cardinal.instLECardinal.{max u3 u4} (Cardinal.lift.{u3, u4} (LinearMap.rank.{u1, u2, u4} K V V'' _inst_1 _inst_2 _inst_3 _inst_8 _inst_9 (LinearMap.comp.{u1, u1, u1, u2, u3, u4} K K K V V' V'' (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u4} V'' _inst_8) _inst_3 _inst_7 _inst_9 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHomCompTriple.ids.{u1, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) f g))) (Min.min.{max (succ u3) (succ u4)} Cardinal.{max u4 u3} (CanonicallyLinearOrderedAddMonoid.toMin.{max (succ u3) (succ u4)} Cardinal.{max u4 u3} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{max u3 u4}) (Cardinal.lift.{u3, u4} (LinearMap.rank.{u1, u3, u4} K V' V'' _inst_1 _inst_6 _inst_7 _inst_8 _inst_9 f)) (Cardinal.lift.{u4, u3} (LinearMap.rank.{u1, u2, u3} K V V' _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 g)))
+Case conversion may be inaccurate. Consider using '#align linear_map.lift_rank_comp_le LinearMap.lift_rank_comp_leₓ'. -/
 /-- The rank of the composition of two maps is less than the minimum of their ranks. -/
 theorem lift_rank_comp_le (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
     Cardinal.lift.{v'} (rank (f.comp g)) ≤
@@ -1896,6 +1904,12 @@ theorem rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) : rank
 #align linear_map.rank_comp_le_right LinearMap.rank_comp_le_right
 -/
 
+/- warning: linear_map.rank_comp_le -> LinearMap.rank_comp_le is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} {V'₁ : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] [_inst_10 : AddCommGroup.{u3} V'₁] [_inst_11 : Module.{u1, u3} K V'₁ (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V'₁ _inst_10)] (g : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (f : LinearMap.{u1, u1, u3, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) V' V'₁ (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u3} V'₁ _inst_10) _inst_7 _inst_11), LE.le.{succ u3} Cardinal.{u3} Cardinal.hasLe.{u3} (LinearMap.rank.{u1, u2, u3} K V V'₁ _inst_1 _inst_2 _inst_3 _inst_10 _inst_11 (LinearMap.comp.{u1, u1, u1, u2, u3, u3} K K K V V' V'₁ (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u3} V'₁ _inst_10) _inst_3 _inst_7 _inst_11 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomCompTriple.right_ids.{u1, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) f g)) (LinearOrder.min.{succ u3} Cardinal.{u3} Cardinal.linearOrder.{u3} (LinearMap.rank.{u1, u3, u3} K V' V'₁ _inst_1 _inst_6 _inst_7 _inst_10 _inst_11 f) (LinearMap.rank.{u1, u2, u3} K V V' _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 g))
+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} {V'₁ : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] [_inst_10 : AddCommGroup.{u3} V'₁] [_inst_11 : Module.{u1, u3} K V'₁ (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V'₁ _inst_10)] (g : LinearMap.{u1, u1, u2, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) (f : LinearMap.{u1, u1, u3, u3} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) V' V'₁ (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u3} V'₁ _inst_10) _inst_7 _inst_11), LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} (LinearMap.rank.{u1, u2, u3} K V V'₁ _inst_1 _inst_2 _inst_3 _inst_10 _inst_11 (LinearMap.comp.{u1, u1, u1, u2, u3, u3} K K K V V' V'₁ (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) (AddCommGroup.toAddCommMonoid.{u3} V'₁ _inst_10) _inst_3 _inst_7 _inst_11 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHomCompTriple.ids.{u1, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) f g)) (Min.min.{succ u3} Cardinal.{u3} (CanonicallyLinearOrderedAddMonoid.toMin.{succ u3} Cardinal.{u3} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u3}) (LinearMap.rank.{u1, u3, u3} K V' V'₁ _inst_1 _inst_6 _inst_7 _inst_10 _inst_11 f) (LinearMap.rank.{u1, u2, u3} K V V' _inst_1 _inst_2 _inst_3 _inst_6 _inst_7 g))
+Case conversion may be inaccurate. Consider using '#align linear_map.rank_comp_le LinearMap.rank_comp_leₓ'. -/
 /-- The rank of the composition of two maps is less than the minimum of their ranks.
 
 See `lift_rank_comp_le` for the universe-polymorphic version. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ebf83ed9c262adbf983ef64d5e8c2ae94b625f4

@@ -1418,7 +1418,7 @@ variable [Fintype η]
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] {V : Type.{u1}} {η : Type.{u1}} [_inst_16 : Fintype.{u1} η] [_inst_17 : AddCommGroup.{u1} V] [_inst_18 : Module.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17)] [_inst_19 : Module.Free.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u1, u1} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17)) (Pi.Function.module.{u1, u1, u1} η K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18)) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) (Fintype.card.{u1} η _inst_16)) (Module.rank.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] {V : Type.{u1}} {η : Type.{u1}} [_inst_16 : Fintype.{u1} η] [_inst_17 : AddCommGroup.{u1} V] [_inst_18 : Module.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17)] [_inst_19 : Module.Free.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u1, u1} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17)) (Pi.module.{u1, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.12987 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17) (fun (i : η) => _inst_18))) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} (Fintype.card.{u1} η _inst_16)) (Module.rank.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18))
+  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] {V : Type.{u1}} {η : Type.{u1}} [_inst_16 : Fintype.{u1} η] [_inst_17 : AddCommGroup.{u1} V] [_inst_18 : Module.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17)] [_inst_19 : Module.Free.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u1, u1} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17)) (Pi.module.{u1, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.12958 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17) (fun (i : η) => _inst_18))) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} (Fintype.card.{u1} η _inst_16)) (Module.rank.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18))
 Case conversion may be inaccurate. Consider using '#align rank_fun rank_funₓ'. -/
 theorem rank_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] [Module.Free K V] :
     Module.rank K (η → V) = Fintype.card η * Module.rank K V := by
@@ -1429,7 +1429,7 @@ theorem rank_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] [Mod
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {η : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] [_inst_15 : Fintype.{u3} η], Eq.{succ (succ (max u3 u2))} Cardinal.{max u3 u2} (Module.rank.{u1, max u3 u2} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u3, u2} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3)) (Pi.Function.module.{u3, u1, u2} η K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)) (HMul.hMul.{succ (max u3 u2), succ (max u3 u2), succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.{max u3 u2} Cardinal.{max u3 u2} (instHMul.{succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.hasMul.{max u3 u2}) ((fun (a : Type) (b : Type.{succ (max u3 u2)}) [self : HasLiftT.{1, succ (succ (max u3 u2))} a b] => self.0) Nat Cardinal.{max u3 u2} (HasLiftT.mk.{1, succ (succ (max u3 u2))} Nat Cardinal.{max u3 u2} (CoeTCₓ.coe.{1, succ (succ (max u3 u2))} Nat Cardinal.{max u3 u2} (Nat.castCoe.{succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.hasNatCast.{max u3 u2}))) (Fintype.card.{u3} η _inst_15)) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {η : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] [_inst_15 : Fintype.{u3} η], Eq.{max (succ (succ u3)) (succ (succ u2))} Cardinal.{max u3 u2} (Module.rank.{u1, max u3 u2} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u3, u2} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3)) (Pi.module.{u3, u2, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13121 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (fun (i : η) => _inst_4))) (HMul.hMul.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.{max u2 u3} Cardinal.{max u3 u2} (instHMul.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instMulCardinal.{max u3 u2}) (Nat.cast.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instNatCastCardinal.{max u3 u2} (Fintype.card.{u3} η _inst_15)) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)))
+  forall {K : Type.{u1}} {V : Type.{u2}} {η : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] [_inst_15 : Fintype.{u3} η], Eq.{max (succ (succ u3)) (succ (succ u2))} Cardinal.{max u3 u2} (Module.rank.{u1, max u3 u2} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u3, u2} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3)) (Pi.module.{u3, u2, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13092 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (fun (i : η) => _inst_4))) (HMul.hMul.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.{max u2 u3} Cardinal.{max u3 u2} (instHMul.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instMulCardinal.{max u3 u2}) (Nat.cast.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instNatCastCardinal.{max u3 u2} (Fintype.card.{u3} η _inst_15)) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)))
 Case conversion may be inaccurate. Consider using '#align rank_fun_eq_lift_mul rank_fun_eq_lift_mulₓ'. -/
 theorem rank_fun_eq_lift_mul :
     Module.rank K (η → V) =
@@ -1441,7 +1441,7 @@ theorem rank_fun_eq_lift_mul :
 lean 3 declaration is
   forall {K : Type.{u1}} {η : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_15 : Fintype.{u2} η], Eq.{succ (succ (max u2 u1))} Cardinal.{max u2 u1} (Module.rank.{u1, max u2 u1} K (η -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => K) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.Function.module.{u2, u1, u1} η K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) ((fun (a : Type) (b : Type.{succ (max u2 u1)}) [self : HasLiftT.{1, succ (succ (max u2 u1))} a b] => self.0) Nat Cardinal.{max u2 u1} (HasLiftT.mk.{1, succ (succ (max u2 u1))} Nat Cardinal.{max u2 u1} (CoeTCₓ.coe.{1, succ (succ (max u2 u1))} Nat Cardinal.{max u2 u1} (Nat.castCoe.{succ (max u2 u1)} Cardinal.{max u2 u1} Cardinal.hasNatCast.{max u2 u1}))) (Fintype.card.{u2} η _inst_15))
 but is expected to have type
-  forall {K : Type.{u1}} {η : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_15 : Fintype.{u2} η], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (η -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => K) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{u2, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13268 : η) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : η) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1))) (Nat.cast.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instNatCastCardinal.{max u1 u2} (Fintype.card.{u2} η _inst_15))
+  forall {K : Type.{u1}} {η : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_15 : Fintype.{u2} η], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (η -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => K) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{u2, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13239 : η) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : η) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1))) (Nat.cast.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instNatCastCardinal.{max u1 u2} (Fintype.card.{u2} η _inst_15))
 Case conversion may be inaccurate. Consider using '#align rank_fun' rank_fun'ₓ'. -/
 theorem rank_fun' : Module.rank K (η → K) = Fintype.card η := by
   rw [rank_fun_eq_lift_mul, rank_self, Cardinal.lift_one, mul_one, Cardinal.natCast_inj]
@@ -1451,7 +1451,7 @@ theorem rank_fun' : Module.rank K (η → K) = Fintype.card η := by
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K ((Fin n) -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.Function.module.{0, u1, u1} (Fin n) K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K ((Fin n) -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13404 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1))) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)
+  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K ((Fin n) -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13375 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1))) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)
 Case conversion may be inaccurate. Consider using '#align rank_fin_fun rank_fin_funₓ'. -/
 theorem rank_fin_fun (n : ℕ) : Module.rank K (Fin n → K) = n := by simp [rank_fun']
 #align rank_fin_fun rank_fin_fun
@@ -1462,7 +1462,7 @@ end Fintype
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) ((fun (a : Type) (b : Type.{succ u2}) [self : HasLiftT.{1, succ (succ u2)} a b] => self.0) Nat Cardinal.{u2} (HasLiftT.mk.{1, succ (succ u2)} Nat Cardinal.{u2} (CoeTCₓ.coe.{1, succ (succ u2)} Nat Cardinal.{u2} (Nat.castCoe.{succ u2} Cardinal.{u2} Cardinal.hasNatCast.{u2}))) n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (finDimVectorspaceEquiv._proof_1.{u1} K _inst_1) (finDimVectorspaceEquiv._proof_2.{u1} K _inst_1) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.Function.module.{0, u1, u1} (Fin n) K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) (Nat.cast.{succ u2} Cardinal.{u2} Cardinal.instNatCastCardinal.{u2} n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13492 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1)))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) (Nat.cast.{succ u2} Cardinal.{u2} Cardinal.instNatCastCardinal.{u2} n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13463 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1)))
 Case conversion may be inaccurate. Consider using '#align fin_dim_vectorspace_equiv finDimVectorspaceEquivₓ'. -/
 -- TODO: merge with the `finrank` content
 /-- An `n`-dimensional `K`-vector space is equivalent to `fin n → K`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ebf83ed9c262adbf983ef64d5e8c2ae94b625f4

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 
 ! This file was ported from Lean 3 source module linear_algebra.dimension
-! leanprover-community/mathlib commit b5b5dd5a47b5744260e2c9185013075ce9dadccd
+! leanprover-community/mathlib commit 47a5f8186becdbc826190ced4312f8199f9db6a5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1876,14 +1876,34 @@ theorem rank_comp_le_left (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') : rank (f.
 #align linear_map.rank_comp_le_left LinearMap.rank_comp_le_left
 -/
 
+theorem lift_rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
+    Cardinal.lift.{v'} (rank (f.comp g)) ≤ Cardinal.lift.{v''} (rank g) := by
+  rw [rank, rank, LinearMap.range_comp] <;> exact lift_rank_map_le _ _
+#align linear_map.lift_rank_comp_le_right LinearMap.lift_rank_comp_le_right
+
+/-- The rank of the composition of two maps is less than the minimum of their ranks. -/
+theorem lift_rank_comp_le (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
+    Cardinal.lift.{v'} (rank (f.comp g)) ≤
+      min (Cardinal.lift.{v'} (rank f)) (Cardinal.lift.{v''} (rank g)) :=
+  le_min (Cardinal.lift_le.mpr <| rank_comp_le_left _ _) (lift_rank_comp_le_right _ _)
+#align linear_map.lift_rank_comp_le LinearMap.lift_rank_comp_le
+
 variable [AddCommGroup V'₁] [Module K V'₁]
 
 #print LinearMap.rank_comp_le_right /-
 theorem rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) : rank (f.comp g) ≤ rank g := by
-  rw [rank, rank, LinearMap.range_comp] <;> exact rank_map_le _ _
+  simpa only [Cardinal.lift_id] using lift_rank_comp_le_right g f
 #align linear_map.rank_comp_le_right LinearMap.rank_comp_le_right
 -/
 
+/-- The rank of the composition of two maps is less than the minimum of their ranks.
+
+See `lift_rank_comp_le` for the universe-polymorphic version. -/
+theorem rank_comp_le (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) :
+    rank (f.comp g) ≤ min (rank f) (rank g) := by
+  simpa only [Cardinal.lift_id] using lift_rank_comp_le g f
+#align linear_map.rank_comp_le LinearMap.rank_comp_le
+
 end Ring
 
 section DivisionRing

mathlib commit https://github.com/leanprover-community/mathlib/commit/347636a7a80595d55bedf6e6fbd996a3c39da69a

@@ -974,6 +974,12 @@ theorem linearIndependent_le_span {ι : Type _} (v : ι → M) (i : LinearIndepe
   exact le_top
 #align linear_independent_le_span linearIndependent_le_span
 
+/- warning: linear_independent_le_span_finset -> linearIndependent_le_span_finset is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}} (v : ι -> M), (LinearIndependent.{u3, u1, u2} ι R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (forall (w : Finset.{u2} M), (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 ((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))) w)) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) -> (LE.le.{succ u3} Cardinal.{u3} Cardinal.hasLe.{u3} (Cardinal.mk.{u3} ι) ((fun (a : Type) (b : Type.{succ u3}) [self : HasLiftT.{1, succ (succ u3)} a b] => self.0) Nat Cardinal.{u3} (HasLiftT.mk.{1, succ (succ u3)} Nat Cardinal.{u3} (CoeTCₓ.coe.{1, succ (succ u3)} Nat Cardinal.{u3} (Nat.castCoe.{succ u3} Cardinal.{u3} Cardinal.hasNatCast.{u3}))) (Finset.card.{u2} M w))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] [_inst_2 : StrongRankCondition.{u2} R (Ring.toSemiring.{u2} R _inst_1)] {M : Type.{u3}} [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] {ι : Type.{u1}} (v : ι -> M), (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) -> (forall (w : Finset.{u3} M), (Eq.{succ u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4 (Finset.toSet.{u3} M w)) (Top.top.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (Submodule.instTopSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4))) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} ι) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} (Finset.card.{u3} M w))))
+Case conversion may be inaccurate. Consider using '#align linear_independent_le_span_finset linearIndependent_le_span_finsetₓ'. -/
 /-- A version of `linear_independent_le_span` for `finset`. -/
 theorem linearIndependent_le_span_finset {ι : Type _} (v : ι → M) (i : LinearIndependent R v)
     (w : Finset M) (s : span R (w : Set M) = ⊤) : (#ι) ≤ w.card := by
@@ -1412,7 +1418,7 @@ variable [Fintype η]
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] {V : Type.{u1}} {η : Type.{u1}} [_inst_16 : Fintype.{u1} η] [_inst_17 : AddCommGroup.{u1} V] [_inst_18 : Module.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17)] [_inst_19 : Module.Free.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u1, u1} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17)) (Pi.Function.module.{u1, u1, u1} η K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18)) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) (Fintype.card.{u1} η _inst_16)) (Module.rank.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] {V : Type.{u1}} {η : Type.{u1}} [_inst_16 : Fintype.{u1} η] [_inst_17 : AddCommGroup.{u1} V] [_inst_18 : Module.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17)] [_inst_19 : Module.Free.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u1, u1} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17)) (Pi.module.{u1, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.12916 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17) (fun (i : η) => _inst_18))) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} (Fintype.card.{u1} η _inst_16)) (Module.rank.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18))
+  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] {V : Type.{u1}} {η : Type.{u1}} [_inst_16 : Fintype.{u1} η] [_inst_17 : AddCommGroup.{u1} V] [_inst_18 : Module.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17)] [_inst_19 : Module.Free.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u1, u1} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17)) (Pi.module.{u1, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.12987 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17) (fun (i : η) => _inst_18))) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} (Fintype.card.{u1} η _inst_16)) (Module.rank.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18))
 Case conversion may be inaccurate. Consider using '#align rank_fun rank_funₓ'. -/
 theorem rank_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] [Module.Free K V] :
     Module.rank K (η → V) = Fintype.card η * Module.rank K V := by
@@ -1423,7 +1429,7 @@ theorem rank_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] [Mod
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {η : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] [_inst_15 : Fintype.{u3} η], Eq.{succ (succ (max u3 u2))} Cardinal.{max u3 u2} (Module.rank.{u1, max u3 u2} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u3, u2} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3)) (Pi.Function.module.{u3, u1, u2} η K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)) (HMul.hMul.{succ (max u3 u2), succ (max u3 u2), succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.{max u3 u2} Cardinal.{max u3 u2} (instHMul.{succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.hasMul.{max u3 u2}) ((fun (a : Type) (b : Type.{succ (max u3 u2)}) [self : HasLiftT.{1, succ (succ (max u3 u2))} a b] => self.0) Nat Cardinal.{max u3 u2} (HasLiftT.mk.{1, succ (succ (max u3 u2))} Nat Cardinal.{max u3 u2} (CoeTCₓ.coe.{1, succ (succ (max u3 u2))} Nat Cardinal.{max u3 u2} (Nat.castCoe.{succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.hasNatCast.{max u3 u2}))) (Fintype.card.{u3} η _inst_15)) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {η : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] [_inst_15 : Fintype.{u3} η], Eq.{max (succ (succ u3)) (succ (succ u2))} Cardinal.{max u3 u2} (Module.rank.{u1, max u3 u2} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u3, u2} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3)) (Pi.module.{u3, u2, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13050 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (fun (i : η) => _inst_4))) (HMul.hMul.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.{max u2 u3} Cardinal.{max u3 u2} (instHMul.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instMulCardinal.{max u3 u2}) (Nat.cast.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instNatCastCardinal.{max u3 u2} (Fintype.card.{u3} η _inst_15)) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)))
+  forall {K : Type.{u1}} {V : Type.{u2}} {η : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] [_inst_15 : Fintype.{u3} η], Eq.{max (succ (succ u3)) (succ (succ u2))} Cardinal.{max u3 u2} (Module.rank.{u1, max u3 u2} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u3, u2} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3)) (Pi.module.{u3, u2, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13121 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (fun (i : η) => _inst_4))) (HMul.hMul.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.{max u2 u3} Cardinal.{max u3 u2} (instHMul.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instMulCardinal.{max u3 u2}) (Nat.cast.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instNatCastCardinal.{max u3 u2} (Fintype.card.{u3} η _inst_15)) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)))
 Case conversion may be inaccurate. Consider using '#align rank_fun_eq_lift_mul rank_fun_eq_lift_mulₓ'. -/
 theorem rank_fun_eq_lift_mul :
     Module.rank K (η → V) =
@@ -1435,7 +1441,7 @@ theorem rank_fun_eq_lift_mul :
 lean 3 declaration is
   forall {K : Type.{u1}} {η : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_15 : Fintype.{u2} η], Eq.{succ (succ (max u2 u1))} Cardinal.{max u2 u1} (Module.rank.{u1, max u2 u1} K (η -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => K) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.Function.module.{u2, u1, u1} η K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) ((fun (a : Type) (b : Type.{succ (max u2 u1)}) [self : HasLiftT.{1, succ (succ (max u2 u1))} a b] => self.0) Nat Cardinal.{max u2 u1} (HasLiftT.mk.{1, succ (succ (max u2 u1))} Nat Cardinal.{max u2 u1} (CoeTCₓ.coe.{1, succ (succ (max u2 u1))} Nat Cardinal.{max u2 u1} (Nat.castCoe.{succ (max u2 u1)} Cardinal.{max u2 u1} Cardinal.hasNatCast.{max u2 u1}))) (Fintype.card.{u2} η _inst_15))
 but is expected to have type
-  forall {K : Type.{u1}} {η : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_15 : Fintype.{u2} η], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (η -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => K) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{u2, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13197 : η) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : η) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1))) (Nat.cast.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instNatCastCardinal.{max u1 u2} (Fintype.card.{u2} η _inst_15))
+  forall {K : Type.{u1}} {η : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_15 : Fintype.{u2} η], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (η -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => K) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{u2, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13268 : η) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : η) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1))) (Nat.cast.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instNatCastCardinal.{max u1 u2} (Fintype.card.{u2} η _inst_15))
 Case conversion may be inaccurate. Consider using '#align rank_fun' rank_fun'ₓ'. -/
 theorem rank_fun' : Module.rank K (η → K) = Fintype.card η := by
   rw [rank_fun_eq_lift_mul, rank_self, Cardinal.lift_one, mul_one, Cardinal.natCast_inj]
@@ -1445,7 +1451,7 @@ theorem rank_fun' : Module.rank K (η → K) = Fintype.card η := by
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K ((Fin n) -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.Function.module.{0, u1, u1} (Fin n) K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K ((Fin n) -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13333 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1))) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)
+  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K ((Fin n) -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13404 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1))) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)
 Case conversion may be inaccurate. Consider using '#align rank_fin_fun rank_fin_funₓ'. -/
 theorem rank_fin_fun (n : ℕ) : Module.rank K (Fin n → K) = n := by simp [rank_fun']
 #align rank_fin_fun rank_fin_fun
@@ -1456,7 +1462,7 @@ end Fintype
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) ((fun (a : Type) (b : Type.{succ u2}) [self : HasLiftT.{1, succ (succ u2)} a b] => self.0) Nat Cardinal.{u2} (HasLiftT.mk.{1, succ (succ u2)} Nat Cardinal.{u2} (CoeTCₓ.coe.{1, succ (succ u2)} Nat Cardinal.{u2} (Nat.castCoe.{succ u2} Cardinal.{u2} Cardinal.hasNatCast.{u2}))) n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (finDimVectorspaceEquiv._proof_1.{u1} K _inst_1) (finDimVectorspaceEquiv._proof_2.{u1} K _inst_1) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.Function.module.{0, u1, u1} (Fin n) K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1))))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) (Nat.cast.{succ u2} Cardinal.{u2} Cardinal.instNatCastCardinal.{u2} n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13421 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1)))
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) (Nat.cast.{succ u2} Cardinal.{u2} Cardinal.instNatCastCardinal.{u2} n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13492 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1)))
 Case conversion may be inaccurate. Consider using '#align fin_dim_vectorspace_equiv finDimVectorspaceEquivₓ'. -/
 -- TODO: merge with the `finrank` content
 /-- An `n`-dimensional `K`-vector space is equivalent to `fin n → K`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/347636a7a80595d55bedf6e6fbd996a3c39da69a

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 
 ! This file was ported from Lean 3 source module linear_algebra.dimension
-! leanprover-community/mathlib commit 25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e
+! leanprover-community/mathlib commit b5b5dd5a47b5744260e2c9185013075ce9dadccd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -421,7 +421,7 @@ variable {R M}
 
 /- warning: exists_mem_ne_zero_of_rank_pos -> exists_mem_ne_zero_of_rank_pos is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_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_8 : Nontrivial.{u1} R] {s : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3}, (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} (OrderedAddCommMonoid.toPartialOrder.{succ u2} Cardinal.{u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ u2} Cardinal.{u2} (OrderedCommSemiring.toOrderedSemiring.{succ u2} Cardinal.{u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u2} Cardinal.{u2} Cardinal.canonicallyOrderedCommSemiring.{u2})))))) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} 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)) s) (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 s) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 s))) -> (Exists.{succ u2} M (fun (b : M) => And (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)) b s) (Ne.{succ u2} M b (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)))))))))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_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_8 : Nontrivial.{u1} R] {s : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3}, (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} 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)) s) (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 s) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 s))) -> (Exists.{succ u2} M (fun (b : M) => And (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)) b s) (Ne.{succ u2} M b (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)))))))))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_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_8 : Nontrivial.{u1} R] {s : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3}, (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (Zero.toOfNat0.{succ u2} Cardinal.{u2} Cardinal.instZeroCardinal.{u2})) (Module.rank.{u1, u2} R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_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 s)) (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 s) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 s))) -> (Exists.{succ u2} M (fun (b : M) => And (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)) b s) (Ne.{succ u2} M b (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))))))))))
 Case conversion may be inaccurate. Consider using '#align exists_mem_ne_zero_of_rank_pos exists_mem_ne_zero_of_rank_posₓ'. -/
@@ -661,7 +661,7 @@ variable [NoZeroSMulDivisors R M]
 
 /- warning: rank_pos -> rank_pos is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_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))))] [_inst_5 : Nontrivial.{u2} M], LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} (OrderedAddCommMonoid.toPartialOrder.{succ u2} Cardinal.{u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ u2} Cardinal.{u2} (OrderedCommSemiring.toOrderedSemiring.{succ u2} Cardinal.{u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u2} Cardinal.{u2} Cardinal.canonicallyOrderedCommSemiring.{u2})))))) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
+  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))))] [_inst_5 : Nontrivial.{u2} M], LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
 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)] [_inst_4 : NoZeroSMulDivisors.{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))))) (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))))] [_inst_5 : Nontrivial.{u2} M], LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (Zero.toOfNat0.{succ u2} Cardinal.{u2} Cardinal.instZeroCardinal.{u2})) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
 Case conversion may be inaccurate. Consider using '#align rank_pos rank_posₓ'. -/
@@ -709,7 +709,7 @@ theorem rank_zero_iff : Module.rank R M = 0 ↔ Subsingleton M :=
 
 /- warning: rank_pos_iff_exists_ne_zero -> rank_pos_iff_exists_ne_zero is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_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))))] [_inst_5 : Nontrivial.{u1} R], Iff (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} (OrderedAddCommMonoid.toPartialOrder.{succ u2} Cardinal.{u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ u2} Cardinal.{u2} (OrderedCommSemiring.toOrderedSemiring.{succ u2} Cardinal.{u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u2} Cardinal.{u2} Cardinal.canonicallyOrderedCommSemiring.{u2})))))) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Exists.{succ u2} M (fun (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))))))))))
+  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))))] [_inst_5 : Nontrivial.{u1} R], Iff (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Exists.{succ u2} M (fun (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))))))))))
 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)] [_inst_4 : NoZeroSMulDivisors.{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))))) (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))))] [_inst_5 : Nontrivial.{u1} R], Iff (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (Zero.toOfNat0.{succ u2} Cardinal.{u2} Cardinal.instZeroCardinal.{u2})) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Exists.{succ u2} M (fun (x : M) => Ne.{succ u2} M x (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)))))))))
 Case conversion may be inaccurate. Consider using '#align rank_pos_iff_exists_ne_zero rank_pos_iff_exists_ne_zeroₓ'. -/
@@ -721,7 +721,7 @@ theorem rank_pos_iff_exists_ne_zero : 0 < Module.rank R M ↔ ∃ x : M, x ≠ 0
 
 /- warning: rank_pos_iff_nontrivial -> rank_pos_iff_nontrivial is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_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))))] [_inst_5 : Nontrivial.{u1} R], Iff (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} (OrderedAddCommMonoid.toPartialOrder.{succ u2} Cardinal.{u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ u2} Cardinal.{u2} (OrderedCommSemiring.toOrderedSemiring.{succ u2} Cardinal.{u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u2} Cardinal.{u2} Cardinal.canonicallyOrderedCommSemiring.{u2})))))) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Nontrivial.{u2} M)
+  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))))] [_inst_5 : Nontrivial.{u1} R], Iff (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Nontrivial.{u2} M)
 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)] [_inst_4 : NoZeroSMulDivisors.{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))))) (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))))] [_inst_5 : Nontrivial.{u1} R], Iff (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (Zero.toOfNat0.{succ u2} Cardinal.{u2} Cardinal.instZeroCardinal.{u2})) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Nontrivial.{u2} M)
 Case conversion may be inaccurate. Consider using '#align rank_pos_iff_nontrivial rank_pos_iff_nontrivialₓ'. -/
@@ -974,6 +974,12 @@ theorem linearIndependent_le_span {ι : Type _} (v : ι → M) (i : LinearIndepe
   exact le_top
 #align linear_independent_le_span linearIndependent_le_span
 
+/-- A version of `linear_independent_le_span` for `finset`. -/
+theorem linearIndependent_le_span_finset {ι : Type _} (v : ι → M) (i : LinearIndependent R v)
+    (w : Finset M) (s : span R (w : Set M) = ⊤) : (#ι) ≤ w.card := by
+  simpa only [Finset.coe_sort_coe, Fintype.card_coe] using linearIndependent_le_span v i w s
+#align linear_independent_le_span_finset linearIndependent_le_span_finset
+
 /- warning: linear_independent_le_infinite_basis -> linearIndependent_le_infinite_basis is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}}, (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (forall [_inst_5 : Infinite.{succ u3} ι] {κ : Type.{u3}} (v : κ -> M), (LinearIndependent.{u3, u1, u2} κ R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (LE.le.{succ u3} Cardinal.{u3} Cardinal.hasLe.{u3} (Cardinal.mk.{u3} κ) (Cardinal.mk.{u3} ι)))
@@ -1152,7 +1158,7 @@ theorem Basis.mk_eq_rank'.{m} (v : Basis ι R M) :
 
 /- warning: basis.nonempty_fintype_index_of_rank_lt_aleph_0 -> Basis.nonempty_fintype_index_of_rank_lt_aleph0 is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}}, (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} (OrderedAddCommMonoid.toPartialOrder.{succ u2} Cardinal.{u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ u2} Cardinal.{u2} (OrderedCommSemiring.toOrderedSemiring.{succ u2} Cardinal.{u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u2} Cardinal.{u2} Cardinal.canonicallyOrderedCommSemiring.{u2})))))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Cardinal.aleph0.{u2}) -> (Nonempty.{succ u3} (Fintype.{u3} ι))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}}, (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Cardinal.aleph0.{u2}) -> (Nonempty.{succ u3} (Fintype.{u3} ι))
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] [_inst_2 : StrongRankCondition.{u2} R (Ring.toSemiring.{u2} R _inst_1)] {M : Type.{u3}} [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] {ι : Type.{u1}}, (Basis.{u1, u2, u3} ι R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) -> (LT.lt.{succ u3} Cardinal.{u3} (Preorder.toLT.{succ u3} Cardinal.{u3} (PartialOrder.toPreorder.{succ u3} Cardinal.{u3} Cardinal.partialOrder.{u3})) (Module.rank.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) Cardinal.aleph0.{u3}) -> (Nonempty.{succ u1} (Fintype.{u1} ι))
 Case conversion may be inaccurate. Consider using '#align basis.nonempty_fintype_index_of_rank_lt_aleph_0 Basis.nonempty_fintype_index_of_rank_lt_aleph0ₓ'. -/
@@ -1173,7 +1179,7 @@ noncomputable def Basis.fintypeIndexOfRankLtAleph0 {ι : Type _} (b : Basis ι R
 
 /- warning: basis.finite_index_of_rank_lt_aleph_0 -> Basis.finite_index_of_rank_lt_aleph0 is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}} {s : Set.{u3} ι}, (Basis.{u3, u1, u2} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} (OrderedAddCommMonoid.toPartialOrder.{succ u2} Cardinal.{u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ u2} Cardinal.{u2} (OrderedCommSemiring.toOrderedSemiring.{succ u2} Cardinal.{u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u2} Cardinal.{u2} Cardinal.canonicallyOrderedCommSemiring.{u2})))))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Cardinal.aleph0.{u2}) -> (Set.Finite.{u3} ι s)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}} {s : Set.{u3} ι}, (Basis.{u3, u1, u2} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Cardinal.aleph0.{u2}) -> (Set.Finite.{u3} ι s)
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] [_inst_2 : StrongRankCondition.{u2} R (Ring.toSemiring.{u2} R _inst_1)] {M : Type.{u3}} [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] {ι : Type.{u1}} {s : Set.{u1} ι}, (Basis.{u1, u2, u3} (Set.Elem.{u1} ι s) R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) -> (LT.lt.{succ u3} Cardinal.{u3} (Preorder.toLT.{succ u3} Cardinal.{u3} (PartialOrder.toPreorder.{succ u3} Cardinal.{u3} Cardinal.partialOrder.{u3})) (Module.rank.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) Cardinal.aleph0.{u3}) -> (Set.Finite.{u1} ι s)
 Case conversion may be inaccurate. Consider using '#align basis.finite_index_of_rank_lt_aleph_0 Basis.finite_index_of_rank_lt_aleph0ₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

@@ -1406,7 +1406,7 @@ variable [Fintype η]
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] {V : Type.{u1}} {η : Type.{u1}} [_inst_16 : Fintype.{u1} η] [_inst_17 : AddCommGroup.{u1} V] [_inst_18 : Module.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17)] [_inst_19 : Module.Free.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u1, u1} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17)) (Pi.Function.module.{u1, u1, u1} η K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18)) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) (Fintype.card.{u1} η _inst_16)) (Module.rank.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18))
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] {V : Type.{u1}} {η : Type.{u1}} [_inst_16 : Fintype.{u1} η] [_inst_17 : AddCommGroup.{u1} V] [_inst_18 : Module.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17)] [_inst_19 : Module.Free.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u1, u1} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17)) (Pi.module.{u1, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.12915 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17) (fun (i : η) => _inst_18))) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} (Fintype.card.{u1} η _inst_16)) (Module.rank.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18))
+  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] {V : Type.{u1}} {η : Type.{u1}} [_inst_16 : Fintype.{u1} η] [_inst_17 : AddCommGroup.{u1} V] [_inst_18 : Module.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17)] [_inst_19 : Module.Free.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u1, u1} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17)) (Pi.module.{u1, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.12916 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} V _inst_17) (fun (i : η) => _inst_18))) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} (Fintype.card.{u1} η _inst_16)) (Module.rank.{u1, u1} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_17) _inst_18))
 Case conversion may be inaccurate. Consider using '#align rank_fun rank_funₓ'. -/
 theorem rank_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] [Module.Free K V] :
     Module.rank K (η → V) = Fintype.card η * Module.rank K V := by
@@ -1417,7 +1417,7 @@ theorem rank_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] [Mod
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} {η : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] [_inst_15 : Fintype.{u3} η], Eq.{succ (succ (max u3 u2))} Cardinal.{max u3 u2} (Module.rank.{u1, max u3 u2} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u3, u2} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3)) (Pi.Function.module.{u3, u1, u2} η K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)) (HMul.hMul.{succ (max u3 u2), succ (max u3 u2), succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.{max u3 u2} Cardinal.{max u3 u2} (instHMul.{succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.hasMul.{max u3 u2}) ((fun (a : Type) (b : Type.{succ (max u3 u2)}) [self : HasLiftT.{1, succ (succ (max u3 u2))} a b] => self.0) Nat Cardinal.{max u3 u2} (HasLiftT.mk.{1, succ (succ (max u3 u2))} Nat Cardinal.{max u3 u2} (CoeTCₓ.coe.{1, succ (succ (max u3 u2))} Nat Cardinal.{max u3 u2} (Nat.castCoe.{succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.hasNatCast.{max u3 u2}))) (Fintype.card.{u3} η _inst_15)) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)))
 but is expected to have type
-  forall {K : Type.{u1}} {V : Type.{u2}} {η : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] [_inst_15 : Fintype.{u3} η], Eq.{max (succ (succ u3)) (succ (succ u2))} Cardinal.{max u3 u2} (Module.rank.{u1, max u3 u2} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u3, u2} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3)) (Pi.module.{u3, u2, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13049 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (fun (i : η) => _inst_4))) (HMul.hMul.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.{max u2 u3} Cardinal.{max u3 u2} (instHMul.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instMulCardinal.{max u3 u2}) (Nat.cast.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instNatCastCardinal.{max u3 u2} (Fintype.card.{u3} η _inst_15)) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)))
+  forall {K : Type.{u1}} {V : Type.{u2}} {η : Type.{u3}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] [_inst_15 : Fintype.{u3} η], Eq.{max (succ (succ u3)) (succ (succ u2))} Cardinal.{max u3 u2} (Module.rank.{u1, max u3 u2} K (η -> V) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u3, u2} η (fun (ᾰ : η) => V) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3)) (Pi.module.{u3, u2, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13050 : η) => V) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (fun (i : η) => _inst_4))) (HMul.hMul.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.{max u2 u3} Cardinal.{max u3 u2} (instHMul.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instMulCardinal.{max u3 u2}) (Nat.cast.{max (succ u3) (succ u2)} Cardinal.{max u3 u2} Cardinal.instNatCastCardinal.{max u3 u2} (Fintype.card.{u3} η _inst_15)) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4)))
 Case conversion may be inaccurate. Consider using '#align rank_fun_eq_lift_mul rank_fun_eq_lift_mulₓ'. -/
 theorem rank_fun_eq_lift_mul :
     Module.rank K (η → V) =
@@ -1429,7 +1429,7 @@ theorem rank_fun_eq_lift_mul :
 lean 3 declaration is
   forall {K : Type.{u1}} {η : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_15 : Fintype.{u2} η], Eq.{succ (succ (max u2 u1))} Cardinal.{max u2 u1} (Module.rank.{u1, max u2 u1} K (η -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => K) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.Function.module.{u2, u1, u1} η K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) ((fun (a : Type) (b : Type.{succ (max u2 u1)}) [self : HasLiftT.{1, succ (succ (max u2 u1))} a b] => self.0) Nat Cardinal.{max u2 u1} (HasLiftT.mk.{1, succ (succ (max u2 u1))} Nat Cardinal.{max u2 u1} (CoeTCₓ.coe.{1, succ (succ (max u2 u1))} Nat Cardinal.{max u2 u1} (Nat.castCoe.{succ (max u2 u1)} Cardinal.{max u2 u1} Cardinal.hasNatCast.{max u2 u1}))) (Fintype.card.{u2} η _inst_15))
 but is expected to have type
-  forall {K : Type.{u1}} {η : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_15 : Fintype.{u2} η], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (η -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => K) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{u2, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13196 : η) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : η) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1))) (Nat.cast.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instNatCastCardinal.{max u1 u2} (Fintype.card.{u2} η _inst_15))
+  forall {K : Type.{u1}} {η : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_15 : Fintype.{u2} η], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (η -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => K) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{u2, u1, u1} η (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13197 : η) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : η) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1))) (Nat.cast.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instNatCastCardinal.{max u1 u2} (Fintype.card.{u2} η _inst_15))
 Case conversion may be inaccurate. Consider using '#align rank_fun' rank_fun'ₓ'. -/
 theorem rank_fun' : Module.rank K (η → K) = Fintype.card η := by
   rw [rank_fun_eq_lift_mul, rank_self, Cardinal.lift_one, mul_one, Cardinal.natCast_inj]
@@ -1439,7 +1439,7 @@ theorem rank_fun' : Module.rank K (η → K) = Fintype.card η := by
 lean 3 declaration is
   forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K ((Fin n) -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.Function.module.{0, u1, u1} (Fin n) K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1)))) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)
 but is expected to have type
-  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K ((Fin n) -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13332 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1))) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)
+  forall {K : Type.{u1}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{u1, u1} K ((Fin n) -> K) (Ring.toSemiring.{u1} K _inst_1) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13333 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1))) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)
 Case conversion may be inaccurate. Consider using '#align rank_fin_fun rank_fin_funₓ'. -/
 theorem rank_fin_fun (n : ℕ) : Module.rank K (Fin n → K) = n := by simp [rank_fun']
 #align rank_fin_fun rank_fin_fun
@@ -1450,7 +1450,7 @@ end Fintype
 lean 3 declaration is
   forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) ((fun (a : Type) (b : Type.{succ u2}) [self : HasLiftT.{1, succ (succ u2)} a b] => self.0) Nat Cardinal.{u2} (HasLiftT.mk.{1, succ (succ u2)} Nat Cardinal.{u2} (CoeTCₓ.coe.{1, succ (succ u2)} Nat Cardinal.{u2} (Nat.castCoe.{succ u2} Cardinal.{u2} Cardinal.hasNatCast.{u2}))) n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (finDimVectorspaceEquiv._proof_1.{u1} K _inst_1) (finDimVectorspaceEquiv._proof_2.{u1} K _inst_1) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.Function.module.{0, u1, u1} (Fin n) K K (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toAddCommGroup.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (Semiring.toModule.{u1} K (Ring.toSemiring.{u1} K _inst_1))))
 but is expected to have type
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+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : Ring.{u1} K] [_inst_2 : StrongRankCondition.{u1} K (Ring.toSemiring.{u1} K _inst_1)] [_inst_3 : AddCommGroup.{u2} V] [_inst_4 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3)] [_inst_5 : Module.Free.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4] (n : Nat), (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) _inst_4) (Nat.cast.{succ u2} Cardinal.{u2} Cardinal.instNatCastCardinal.{u2} n)) -> (LinearEquiv.{u1, u1, u2, u1} K K (Ring.toSemiring.{u1} K _inst_1) (Ring.toSemiring.{u1} K _inst_1) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K _inst_1))) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) (RingHomInvPair.ids.{u1} K (Ring.toSemiring.{u1} K _inst_1)) V ((Fin n) -> K) (AddCommGroup.toAddCommMonoid.{u2} V _inst_3) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => K) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1))))) _inst_4 (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.LinearAlgebra.Dimension._hyg.13421 : Fin n) => K) K (Ring.toSemiring.{u1} K _inst_1) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K _inst_1)))) (fun (i : Fin n) => instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} K _inst_1)))
 Case conversion may be inaccurate. Consider using '#align fin_dim_vectorspace_equiv finDimVectorspaceEquivₓ'. -/
 -- TODO: merge with the `finrank` content
 /-- An `n`-dimensional `K`-vector space is equivalent to `fin n → K`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 
 ! This file was ported from Lean 3 source module linear_algebra.dimension
-! leanprover-community/mathlib commit 45ce3929e3bf9a086a216feea3b1ab6c14bf0e67
+! leanprover-community/mathlib commit 25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -19,6 +19,9 @@ import Mathbin.SetTheory.Cardinal.Cofinality
 /-!
 # Dimension of modules and vector spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main definitions
 
 * The rank of a module is defined as `module.rank : cardinal`.

mathlib commit https://github.com/leanprover-community/mathlib/commit/e05ead7993520a432bec94ac504842d90707ad63

@@ -98,6 +98,7 @@ include K
 
 variable (K V)
 
+#print Module.rank /-
 /-- The rank of a module, defined as a term of type `cardinal`.
 
 We define this as the supremum of the cardinalities of linearly independent subsets.
@@ -114,6 +115,7 @@ the rank of a linear map.
 protected irreducible_def Module.rank : Cardinal :=
   ⨆ ι : { s : Set V // LinearIndependent K (coe : s → V) }, #ι.1
 #align module.rank Module.rank
+-/
 
 end
 
@@ -127,6 +129,12 @@ variable {M' : Type v'} [AddCommGroup M'] [Module R M']
 
 variable {M₁ : Type v} [AddCommGroup M₁] [Module R M₁]
 
+/- warning: linear_map.lift_rank_le_of_injective -> LinearMap.lift_rank_le_of_injective 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.lift_rank_le_of_injective LinearMap.lift_rank_le_of_injectiveₓ'. -/
 theorem LinearMap.lift_rank_le_of_injective (f : M →ₗ[R] M') (i : Injective f) :
     Cardinal.lift.{v'} (Module.rank R M) ≤ Cardinal.lift.{v} (Module.rank R M') :=
   by
@@ -139,11 +147,23 @@ theorem LinearMap.lift_rank_le_of_injective (f : M →ₗ[R] M') (i : Injective
   exact (li.map' _ <| linear_map.ker_eq_bot.mpr i).image
 #align linear_map.lift_rank_le_of_injective LinearMap.lift_rank_le_of_injective
 
+/- warning: linear_map.rank_le_of_injective -> LinearMap.rank_le_of_injective is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.rank_le_of_injective LinearMap.rank_le_of_injectiveₓ'. -/
 theorem LinearMap.rank_le_of_injective (f : M →ₗ[R] M₁) (i : Injective f) :
     Module.rank R M ≤ Module.rank R M₁ :=
   Cardinal.lift_le.1 (f.lift_rank_le_of_injective i)
 #align linear_map.rank_le_of_injective LinearMap.rank_le_of_injective
 
+/- warning: rank_le -> rank_le is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align rank_le rank_leₓ'. -/
 theorem rank_le {n : ℕ}
     (H : ∀ s : Finset M, (LinearIndependent R fun i : s => (i : M)) → s.card ≤ n) :
     Module.rank R M ≤ n := by
@@ -153,6 +173,12 @@ theorem rank_le {n : ℕ}
   exact linearIndependent_bounded_of_finset_linearIndependent_bounded H _ li
 #align rank_le rank_le
 
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+Case conversion may be inaccurate. Consider using '#align lift_rank_range_le lift_rank_range_leₓ'. -/
 theorem lift_rank_range_le (f : M →ₗ[R] M') :
     Cardinal.lift.{v} (Module.rank R f.range) ≤ Cardinal.lift.{v'} (Module.rank R M) :=
   by
@@ -169,10 +195,22 @@ theorem lift_rank_range_le (f : M →ₗ[R] M') :
   · exact (cardinal.lift_mk_eq'.mpr ⟨Equiv.Set.rangeSplittingImageEquiv f s⟩).ge
 #align lift_rank_range_le lift_rank_range_le
 
+/- warning: rank_range_le -> rank_range_le 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 rank_range_le rank_range_leₓ'. -/
 theorem rank_range_le (f : M →ₗ[R] M₁) : Module.rank R f.range ≤ Module.rank R M := by
   simpa using lift_rank_range_le f
 #align rank_range_le rank_range_le
 
+/- warning: lift_rank_map_le -> lift_rank_map_le 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 lift_rank_map_le lift_rank_map_leₓ'. -/
 theorem lift_rank_map_le (f : M →ₗ[R] M') (p : Submodule R M) :
     Cardinal.lift.{v} (Module.rank R (p.map f)) ≤ Cardinal.lift.{v'} (Module.rank R p) :=
   by
@@ -180,16 +218,29 @@ theorem lift_rank_map_le (f : M →ₗ[R] M') (p : Submodule R M) :
   rwa [LinearMap.range_comp, range_subtype] at h
 #align lift_rank_map_le lift_rank_map_le
 
+/- warning: rank_map_le -> rank_map_le is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align rank_map_le rank_map_leₓ'. -/
 theorem rank_map_le (f : M →ₗ[R] M₁) (p : Submodule R M) :
     Module.rank R (p.map f) ≤ Module.rank R p := by simpa using lift_rank_map_le f p
 #align rank_map_le rank_map_le
 
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+Case conversion may be inaccurate. Consider using '#align rank_le_of_submodule rank_le_of_submoduleₓ'. -/
 theorem rank_le_of_submodule (s t : Submodule R M) (h : s ≤ t) :
     Module.rank R s ≤ Module.rank R t :=
   (ofLe h).rank_le_of_injective fun ⟨x, hx⟩ ⟨y, hy⟩ eq =>
     Subtype.eq <| show x = y from Subtype.ext_iff_val.1 Eq
 #align rank_le_of_submodule rank_le_of_submodule
 
+#print LinearEquiv.lift_rank_eq /-
 /-- Two linearly equivalent vector spaces have the same dimension, a version with different
 universes. -/
 theorem LinearEquiv.lift_rank_eq (f : M ≃ₗ[R] M') :
@@ -199,17 +250,32 @@ theorem LinearEquiv.lift_rank_eq (f : M ≃ₗ[R] M') :
   · exact f.to_linear_map.lift_rank_le_of_injective f.injective
   · exact f.symm.to_linear_map.lift_rank_le_of_injective f.symm.injective
 #align linear_equiv.lift_rank_eq LinearEquiv.lift_rank_eq
+-/
 
+#print LinearEquiv.rank_eq /-
 /-- Two linearly equivalent vector spaces have the same dimension. -/
 theorem LinearEquiv.rank_eq (f : M ≃ₗ[R] M₁) : Module.rank R M = Module.rank R M₁ :=
   Cardinal.lift_inj.1 f.lift_rank_eq
 #align linear_equiv.rank_eq LinearEquiv.rank_eq
+-/
 
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+Case conversion may be inaccurate. Consider using '#align rank_eq_of_injective rank_eq_of_injectiveₓ'. -/
 theorem rank_eq_of_injective (f : M →ₗ[R] M₁) (h : Injective f) :
     Module.rank R M = Module.rank R f.range :=
   (LinearEquiv.ofInjective f h).rank_eq
 #align rank_eq_of_injective rank_eq_of_injective
 
+/- warning: linear_equiv.rank_map_eq -> LinearEquiv.rank_map_eq is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) x p)) (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 p) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 p))
+Case conversion may be inaccurate. Consider using '#align linear_equiv.rank_map_eq LinearEquiv.rank_map_eqₓ'. -/
 /-- Pushforwards of submodules along a `linear_equiv` have the same dimension. -/
 theorem LinearEquiv.rank_map_eq (f : M ≃ₗ[R] M₁) (p : Submodule R M) :
     Module.rank R (p.map (f : M →ₗ[R] M₁)) = Module.rank R p :=
@@ -218,6 +284,12 @@ theorem LinearEquiv.rank_map_eq (f : M ≃ₗ[R] M₁) (p : Submodule R M) :
 
 variable (R M)
 
+/- warning: rank_top -> rank_top is a dubious translation:
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 @[simp]
 theorem rank_top : Module.rank R (⊤ : Submodule R M) = Module.rank R M :=
   by
@@ -227,16 +299,30 @@ theorem rank_top : Module.rank R (⊤ : Submodule R M) = Module.rank R M :=
 
 variable {R M}
 
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+Case conversion may be inaccurate. Consider using '#align rank_range_of_surjective rank_range_of_surjectiveₓ'. -/
 theorem rank_range_of_surjective (f : M →ₗ[R] M') (h : Surjective f) :
     Module.rank R f.range = Module.rank R M' := by rw [LinearMap.range_eq_top.2 h, rank_top]
 #align rank_range_of_surjective rank_range_of_surjective
 
+#print rank_submodule_le /-
 theorem rank_submodule_le (s : Submodule R M) : Module.rank R s ≤ Module.rank R M :=
   by
   rw [← rank_top R M]
   exact rank_le_of_submodule _ _ le_top
 #align rank_submodule_le rank_submodule_le
+-/
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.rank_le_of_surjective LinearMap.rank_le_of_surjectiveₓ'. -/
 theorem LinearMap.rank_le_of_surjective (f : M →ₗ[R] M₁) (h : Surjective f) :
     Module.rank R M₁ ≤ Module.rank R M :=
   by
@@ -244,12 +330,20 @@ theorem LinearMap.rank_le_of_surjective (f : M →ₗ[R] M₁) (h : Surjective f
   apply rank_range_le
 #align linear_map.rank_le_of_surjective LinearMap.rank_le_of_surjective
 
+#print rank_quotient_le /-
 theorem rank_quotient_le (p : Submodule R M) : Module.rank R (M ⧸ p) ≤ Module.rank R M :=
   (mkQ p).rank_le_of_surjective (surjective_quot_mk _)
 #align rank_quotient_le rank_quotient_le
+-/
 
 variable [Nontrivial R]
 
+/- warning: cardinal_lift_le_rank_of_linear_independent -> cardinal_lift_le_rank_of_linearIndependent is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal_lift_le_rank_of_linear_independent cardinal_lift_le_rank_of_linearIndependentₓ'. -/
 theorem cardinal_lift_le_rank_of_linearIndependent.{m} {ι : Type w} {v : ι → M}
     (hv : LinearIndependent R v) :
     Cardinal.lift.{max v m} (#ι) ≤ Cardinal.lift.{max w m} (Module.rank R M) :=
@@ -263,25 +357,37 @@ theorem cardinal_lift_le_rank_of_linearIndependent.{m} {ι : Type w} {v : ι →
     exact le_rfl
 #align cardinal_lift_le_rank_of_linear_independent cardinal_lift_le_rank_of_linearIndependent
 
-theorem cardinal_lift_le_rank_of_linear_independent' {ι : Type w} {v : ι → M}
+#print cardinal_lift_le_rank_of_linearIndependent' /-
+theorem cardinal_lift_le_rank_of_linearIndependent' {ι : Type w} {v : ι → M}
     (hv : LinearIndependent R v) : Cardinal.lift.{v} (#ι) ≤ Cardinal.lift.{w} (Module.rank R M) :=
   cardinal_lift_le_rank_of_linearIndependent.{u, v, w, 0} hv
-#align cardinal_lift_le_rank_of_linear_independent' cardinal_lift_le_rank_of_linear_independent'
+#align cardinal_lift_le_rank_of_linear_independent' cardinal_lift_le_rank_of_linearIndependent'
+-/
 
+#print cardinal_le_rank_of_linearIndependent /-
 theorem cardinal_le_rank_of_linearIndependent {ι : Type v} {v : ι → M}
     (hv : LinearIndependent R v) : (#ι) ≤ Module.rank R M := by
   simpa using cardinal_lift_le_rank_of_linearIndependent hv
 #align cardinal_le_rank_of_linear_independent cardinal_le_rank_of_linearIndependent
+-/
 
-theorem cardinal_le_rank_of_linear_independent' {s : Set M}
+#print cardinal_le_rank_of_linearIndependent' /-
+theorem cardinal_le_rank_of_linearIndependent' {s : Set M}
     (hs : LinearIndependent R (fun x => x : s → M)) : (#s) ≤ Module.rank R M :=
   cardinal_le_rank_of_linearIndependent hs
-#align cardinal_le_rank_of_linear_independent' cardinal_le_rank_of_linear_independent'
+#align cardinal_le_rank_of_linear_independent' cardinal_le_rank_of_linearIndependent'
+-/
 
 variable (R M)
 
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+Case conversion may be inaccurate. Consider using '#align rank_punit rank_punitₓ'. -/
 @[simp]
-theorem rank_pUnit : Module.rank R PUnit = 0 :=
+theorem rank_punit : Module.rank R PUnit = 0 :=
   by
   apply le_bot_iff.mp
   rw [Module.rank]
@@ -293,22 +399,35 @@ theorem rank_pUnit : Module.rank R PUnit = 0 :=
   by_contra h
   obtain ⟨a, ha⟩ := nonempty_iff_ne_empty.2 h
   simpa using LinearIndependent.ne_zero (⟨a, ha⟩ : s) li
-#align rank_punit rank_pUnit
-
+#align rank_punit rank_punit
+
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+Case conversion may be inaccurate. Consider using '#align rank_bot rank_botₓ'. -/
 @[simp]
 theorem rank_bot : Module.rank R (⊥ : Submodule R M) = 0 :=
   by
   have : (⊥ : Submodule R M) ≃ₗ[R] PUnit := bot_equiv_punit
-  rw [this.rank_eq, rank_pUnit]
+  rw [this.rank_eq, rank_punit]
 #align rank_bot rank_bot
 
 variable {R M}
 
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+Case conversion may be inaccurate. Consider using '#align exists_mem_ne_zero_of_rank_pos exists_mem_ne_zero_of_rank_posₓ'. -/
 theorem exists_mem_ne_zero_of_rank_pos {s : Submodule R M} (h : 0 < Module.rank R s) :
     ∃ b : M, b ∈ s ∧ b ≠ 0 :=
   exists_mem_ne_zero_of_ne_bot fun eq => by rw [Eq, rank_bot] at h <;> exact lt_irrefl _ h
 #align exists_mem_ne_zero_of_rank_pos exists_mem_ne_zero_of_rank_pos
 
+#print LinearIndependent.finite_of_isNoetherian /-
 /-- A linearly-independent family of vectors in a module over a non-trivial ring must be finite if
 the module is Noetherian. -/
 theorem LinearIndependent.finite_of_isNoetherian [IsNoetherian R M] {v : ι → M}
@@ -322,12 +441,21 @@ theorem LinearIndependent.finite_of_isNoetherian [IsNoetherian R M] {v : ι →
   have : v i ∈ R ∙ v i := Submodule.mem_span_singleton_self (v i)
   rwa [contra, Submodule.mem_bot] at this
 #align linear_independent.finite_of_is_noetherian LinearIndependent.finite_of_isNoetherian
+-/
 
+#print LinearIndependent.set_finite_of_isNoetherian /-
 theorem LinearIndependent.set_finite_of_isNoetherian [IsNoetherian R M] {s : Set M}
     (hi : LinearIndependent R (coe : s → M)) : s.Finite :=
   @Set.toFinite _ _ hi.finite_of_isNoetherian
 #align linear_independent.set_finite_of_is_noetherian LinearIndependent.set_finite_of_isNoetherian
+-/
 
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+Case conversion may be inaccurate. Consider using '#align basis_fintype_of_finite_spans basisFintypeOfFiniteSpansₓ'. -/
 -- One might hope that a finite spanning set implies that any linearly independent set is finite.
 -- While this is true over a division ring
 -- (simply because any linearly independent set can be extended to a basis),
@@ -366,6 +494,12 @@ def basisFintypeOfFiniteSpans (w : Set M) [Fintype w] (s : span R w = ⊤) {ι :
   exact nm
 #align basis_fintype_of_finite_spans basisFintypeOfFiniteSpans
 
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(Ring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R M (Finsupp.{u3, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Basis.repr.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b) (v k))))) (Set.univ.{u3} ι))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_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_8 : Nontrivial.{u1} R] {ι : Type.{u3}} (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) {κ : Type.{u4}} (v : κ -> M) (i : LinearIndependent.{u4, u1, u2} κ R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3), (LinearIndependent.Maximal.{u1, u2, u4} κ R (Ring.toSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 v i) -> (Eq.{succ u3} (Set.{u3} ι) (Set.unionᵢ.{u3, succ u4} ι κ (fun (k : κ) => Finset.toSet.{u3} ι (Finsupp.support.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{max u1 u3} (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Module.toDistribMulAction.{u1, max u1 u3} R (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R M (Finsupp.{u3, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (Finsupp.addCommMonoid.{u3, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u1, u1} ι R R (Ring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (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))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 b) (v k))))) (Set.univ.{u3} ι))
+Case conversion may be inaccurate. Consider using '#align union_support_maximal_linear_independent_eq_range_basis union_support_maximal_linearIndependent_eq_range_basisₓ'. -/
 -- From [Les familles libres maximales d'un module ont-elles le meme cardinal?][lazarus1973]
 /-- Over any ring `R`, if `b` is a basis for a module `M`,
 and `s` is a maximal linearly independent set,
@@ -440,11 +574,12 @@ theorem union_support_maximal_linearIndependent_eq_range_basis {ι : Type w} (b
   exact r'' m
 #align union_support_maximal_linear_independent_eq_range_basis union_support_maximal_linearIndependent_eq_range_basis
 
+#print infinite_basis_le_maximal_linearIndependent' /-
 /-- Over any ring `R`, if `b` is an infinite basis for a module `M`,
 and `s` is a maximal linearly independent set,
 then the cardinality of `b` is bounded by the cardinality of `s`.
 -/
-theorem infinite_basis_le_maximal_linear_independent' {ι : Type w} (b : Basis ι R M) [Infinite ι]
+theorem infinite_basis_le_maximal_linearIndependent' {ι : Type w} (b : Basis ι R M) [Infinite ι]
     {κ : Type w'} (v : κ → M) (i : LinearIndependent R v) (m : i.Maximal) :
     Cardinal.lift.{w'} (#ι) ≤ Cardinal.lift.{w} (#κ) :=
   by
@@ -455,8 +590,10 @@ theorem infinite_basis_le_maximal_linear_independent' {ι : Type w} (b : Basis 
     exact union_support_maximal_linearIndependent_eq_range_basis b v i m
   have w₂ : Cardinal.lift.{w'} (#Set.range Φ) ≤ Cardinal.lift.{w} (#κ) := Cardinal.mk_range_le_lift
   exact (cardinal.lift_le.mpr w₁).trans w₂
-#align infinite_basis_le_maximal_linear_independent' infinite_basis_le_maximal_linear_independent'
+#align infinite_basis_le_maximal_linear_independent' infinite_basis_le_maximal_linearIndependent'
+-/
 
+#print infinite_basis_le_maximal_linearIndependent /-
 -- (See `infinite_basis_le_maximal_linear_independent'` for the more general version
 -- where the index types can live in different universes.)
 /-- Over any ring `R`, if `b` is an infinite basis for a module `M`,
@@ -465,9 +602,16 @@ then the cardinality of `b` is bounded by the cardinality of `s`.
 -/
 theorem infinite_basis_le_maximal_linearIndependent {ι : Type w} (b : Basis ι R M) [Infinite ι]
     {κ : Type w} (v : κ → M) (i : LinearIndependent R v) (m : i.Maximal) : (#ι) ≤ (#κ) :=
-  Cardinal.lift_le.mp (infinite_basis_le_maximal_linear_independent' b v i m)
+  Cardinal.lift_le.mp (infinite_basis_le_maximal_linearIndependent' b v i m)
 #align infinite_basis_le_maximal_linear_independent infinite_basis_le_maximal_linearIndependent
+-/
 
+/- warning: complete_lattice.independent.subtype_ne_bot_le_rank -> CompleteLattice.Independent.subtype_ne_bot_le_rank is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u3}} {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_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_8 : Nontrivial.{u1} R] [_inst_9 : 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))))] {V : ι -> (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)}, (CompleteLattice.Independent.{succ u3, u2} ι (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) V) -> (LE.le.{succ (max u3 u2)} Cardinal.{max u3 u2} Cardinal.hasLe.{max u3 u2} (Cardinal.lift.{u2, u3} (Cardinal.mk.{u3} (Subtype.{succ u3} ι (fun (i : ι) => Ne.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (V i) (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {M : Type.{u2}} [_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_8 : Nontrivial.{u1} R] [_inst_9 : NoZeroSMulDivisors.{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))))) (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))))] {V : ι -> (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)}, (CompleteLattice.Independent.{succ u3, u2} ι (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) V) -> (LE.le.{max (succ u2) (succ u3)} Cardinal.{max u3 u2} Cardinal.instLECardinal.{max u2 u3} (Cardinal.lift.{u2, u3} (Cardinal.mk.{u3} (Subtype.{succ u3} ι (fun (i : ι) => Ne.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (V i) (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.instBotSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))) (Cardinal.lift.{u3, u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))
+Case conversion may be inaccurate. Consider using '#align complete_lattice.independent.subtype_ne_bot_le_rank CompleteLattice.Independent.subtype_ne_bot_le_rankₓ'. -/
 theorem CompleteLattice.Independent.subtype_ne_bot_le_rank [NoZeroSMulDivisors R M]
     {V : ι → Submodule R M} (hV : CompleteLattice.Independent V) :
     Cardinal.lift.{v} (#{ i : ι // V i ≠ ⊥ }) ≤ Cardinal.lift.{w} (Module.rank R M) :=
@@ -479,7 +623,7 @@ theorem CompleteLattice.Independent.subtype_ne_bot_le_rank [NoZeroSMulDivisors R
     exact i.prop
   choose v hvV hv using hI
   have : LinearIndependent R v := (hV.comp Subtype.coe_injective).LinearIndependent _ hvV hv
-  exact cardinal_lift_le_rank_of_linear_independent' this
+  exact cardinal_lift_le_rank_of_linearIndependent' this
 #align complete_lattice.independent.subtype_ne_bot_le_rank CompleteLattice.Independent.subtype_ne_bot_le_rank
 
 end
@@ -490,6 +634,7 @@ variable {R : Type u} {M : Type v}
 
 variable [Ring R] [AddCommGroup M] [Module R M]
 
+#print rank_subsingleton /-
 @[simp]
 theorem rank_subsingleton [Subsingleton R] : Module.rank R M = 1 :=
   by
@@ -507,9 +652,16 @@ theorem rank_subsingleton [Subsingleton R] : Module.rank R M = 1 :=
     exact Subsingleton.elim _ _
   · exact hw.trans_eq (Cardinal.mk_singleton _).symm
 #align rank_subsingleton rank_subsingleton
+-/
 
 variable [NoZeroSMulDivisors R M]
 
+/- warning: rank_pos -> rank_pos is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_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))))] [_inst_5 : Nontrivial.{u2} M], LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} (OrderedAddCommMonoid.toPartialOrder.{succ u2} Cardinal.{u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ u2} Cardinal.{u2} (OrderedCommSemiring.toOrderedSemiring.{succ u2} Cardinal.{u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u2} Cardinal.{u2} Cardinal.canonicallyOrderedCommSemiring.{u2})))))) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
+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)] [_inst_4 : NoZeroSMulDivisors.{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))))) (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))))] [_inst_5 : Nontrivial.{u2} M], LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (Zero.toOfNat0.{succ u2} Cardinal.{u2} Cardinal.instZeroCardinal.{u2})) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
+Case conversion may be inaccurate. Consider using '#align rank_pos rank_posₓ'. -/
 theorem rank_pos [Nontrivial M] : 0 < Module.rank R M :=
   by
   obtain ⟨x, hx⟩ := exists_ne (0 : M)
@@ -522,6 +674,12 @@ theorem rank_pos [Nontrivial M] : 0 < Module.rank R M :=
 
 variable [Nontrivial R]
 
+/- warning: rank_zero_iff_forall_zero -> rank_zero_iff_forall_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_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))))] [_inst_5 : Nontrivial.{u1} R], Iff (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2})))) (forall (x : M), Eq.{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)))))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align rank_zero_iff_forall_zero rank_zero_iff_forall_zeroₓ'. -/
 theorem rank_zero_iff_forall_zero : Module.rank R M = 0 ↔ ∀ x : M, x = 0 :=
   by
   refine' ⟨fun h => _, fun h => _⟩
@@ -535,17 +693,35 @@ theorem rank_zero_iff_forall_zero : Module.rank R M = 0 ↔ ∀ x : M, x = 0 :=
     rw [← rank_top, this, rank_bot]
 #align rank_zero_iff_forall_zero rank_zero_iff_forall_zero
 
+/- warning: rank_zero_iff -> rank_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_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))))] [_inst_5 : Nontrivial.{u1} R], Iff (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2})))) (Subsingleton.{succ u2} M)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align rank_zero_iff rank_zero_iffₓ'. -/
 /-- See `rank_subsingleton` for the reason that `nontrivial R` is needed. -/
 theorem rank_zero_iff : Module.rank R M = 0 ↔ Subsingleton M :=
   rank_zero_iff_forall_zero.trans (subsingleton_iff_forall_eq 0).symm
 #align rank_zero_iff rank_zero_iff
 
+/- warning: rank_pos_iff_exists_ne_zero -> rank_pos_iff_exists_ne_zero is a dubious translation:
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+  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))))] [_inst_5 : Nontrivial.{u1} R], Iff (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} (OrderedAddCommMonoid.toPartialOrder.{succ u2} Cardinal.{u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ u2} Cardinal.{u2} (OrderedCommSemiring.toOrderedSemiring.{succ u2} Cardinal.{u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u2} Cardinal.{u2} Cardinal.canonicallyOrderedCommSemiring.{u2})))))) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Exists.{succ u2} M (fun (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))))))))))
+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)] [_inst_4 : NoZeroSMulDivisors.{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))))) (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))))] [_inst_5 : Nontrivial.{u1} R], Iff (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (Zero.toOfNat0.{succ u2} Cardinal.{u2} Cardinal.instZeroCardinal.{u2})) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Exists.{succ u2} M (fun (x : M) => Ne.{succ u2} M x (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)))))))))
+Case conversion may be inaccurate. Consider using '#align rank_pos_iff_exists_ne_zero rank_pos_iff_exists_ne_zeroₓ'. -/
 theorem rank_pos_iff_exists_ne_zero : 0 < Module.rank R M ↔ ∃ x : M, x ≠ 0 :=
   by
   rw [← not_iff_not]
   simpa using rank_zero_iff_forall_zero
 #align rank_pos_iff_exists_ne_zero rank_pos_iff_exists_ne_zero
 
+/- warning: rank_pos_iff_nontrivial -> rank_pos_iff_nontrivial is a dubious translation:
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+  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))))] [_inst_5 : Nontrivial.{u1} R], Iff (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} (OrderedAddCommMonoid.toPartialOrder.{succ u2} Cardinal.{u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ u2} Cardinal.{u2} (OrderedCommSemiring.toOrderedSemiring.{succ u2} Cardinal.{u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u2} Cardinal.{u2} Cardinal.canonicallyOrderedCommSemiring.{u2})))))) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (OfNat.mk.{succ u2} Cardinal.{u2} 0 (Zero.zero.{succ u2} Cardinal.{u2} Cardinal.hasZero.{u2}))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Nontrivial.{u2} M)
+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)] [_inst_4 : NoZeroSMulDivisors.{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))))) (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))))] [_inst_5 : Nontrivial.{u1} R], Iff (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (OfNat.ofNat.{succ u2} Cardinal.{u2} 0 (Zero.toOfNat0.{succ u2} Cardinal.{u2} Cardinal.instZeroCardinal.{u2})) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Nontrivial.{u2} M)
+Case conversion may be inaccurate. Consider using '#align rank_pos_iff_nontrivial rank_pos_iff_nontrivialₓ'. -/
 theorem rank_pos_iff_nontrivial : 0 < Module.rank R M ↔ Nontrivial M :=
   rank_pos_iff_exists_ne_zero.trans (nontrivial_iff_exists_ne 0).symm
 #align rank_pos_iff_nontrivial rank_pos_iff_nontrivial
@@ -558,6 +734,7 @@ variable {R : Type u} [Ring R] [InvariantBasisNumber R]
 
 variable {M : Type v} [AddCommGroup M] [Module R M]
 
+#print mk_eq_mk_of_basis /-
 /-- The dimension theorem: if `v` and `v'` are two bases, their index types
 have the same cardinalities. -/
 theorem mk_eq_mk_of_basis (v : Basis ι R M) (v' : Basis ι' R M) :
@@ -580,22 +757,31 @@ theorem mk_eq_mk_of_basis (v : Basis ι R M) (v' : Basis ι' R M) :
     -- so by `infinite_basis_le_maximal_linear_independent`, `v'` is at least as big,
     -- and then applying `infinite_basis_le_maximal_linear_independent` again
     -- we see they have the same cardinality.
-    have w₁ := infinite_basis_le_maximal_linear_independent' v _ v'.linear_independent v'.maximal
+    have w₁ := infinite_basis_le_maximal_linearIndependent' v _ v'.linear_independent v'.maximal
     rcases cardinal.lift_mk_le'.mp w₁ with ⟨f⟩
     haveI : Infinite ι' := Infinite.of_injective f f.2
-    have w₂ := infinite_basis_le_maximal_linear_independent' v' _ v.linear_independent v.maximal
+    have w₂ := infinite_basis_le_maximal_linearIndependent' v' _ v.linear_independent v.maximal
     exact le_antisymm w₁ w₂
 #align mk_eq_mk_of_basis mk_eq_mk_of_basis
+-/
 
+/- warning: basis.index_equiv -> Basis.indexEquiv is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{w}} {ι' : Type.{w'}} {R : Type.{u}} [_inst_1 : Ring.{u} R] [_inst_2 : InvariantBasisNumber.{u} R (Ring.toSemiring.{u} R _inst_1)] {M : Type.{v}} [_inst_3 : AddCommGroup.{v} M] [_inst_4 : Module.{u, v} R M (Ring.toSemiring.{u} R _inst_1) (AddCommGroup.toAddCommMonoid.{v} M _inst_3)], (Basis.{w, u, v} ι R M (Ring.toSemiring.{u} R _inst_1) (AddCommGroup.toAddCommMonoid.{v} M _inst_3) _inst_4) -> (Basis.{w', u, v} ι' R M (Ring.toSemiring.{u} R _inst_1) (AddCommGroup.toAddCommMonoid.{v} M _inst_3) _inst_4) -> (Equiv.{succ w, succ w'} ι ι')
+but is expected to have type
+  forall {ι : Type.{w}} {ι' : Type.{w'}} {R : Type.{u}} [_inst_1 : Ring.{u} R] [_inst_2 : InvariantBasisNumber.{u} R (Ring.toSemiring.{u} R _inst_1)] {M : Type.{v}} [_inst_3 : AddCommGroup.{v} M] [_inst_4 : Module.{u, v} R M (Ring.toSemiring.{u} R _inst_1) (AddCommGroup.toAddCommMonoid.{v} M _inst_3)], (Basis.{w, u, v} ι R M (Ring.toSemiring.{u} R _inst_1) (AddCommGroup.toAddCommMonoid.{v} M _inst_3) _inst_4) -> (Basis.{w', u, v} ι' R M (Ring.toSemiring.{u} R _inst_1) (AddCommGroup.toAddCommMonoid.{v} M _inst_3) _inst_4) -> (Equiv.{succ w, succ w'} ι ι')
+Case conversion may be inaccurate. Consider using '#align basis.index_equiv Basis.indexEquivₓ'. -/
 /-- Given two bases indexed by `ι` and `ι'` of an `R`-module, where `R` satisfies the invariant
 basis number property, an equiv `ι ≃ ι' `. -/
 def Basis.indexEquiv (v : Basis ι R M) (v' : Basis ι' R M) : ι ≃ ι' :=
   Nonempty.some (Cardinal.lift_mk_eq.1 (Cardinal.lift_umax_eq.2 (mk_eq_mk_of_basis v v')))
 #align basis.index_equiv Basis.indexEquiv
 
+#print mk_eq_mk_of_basis' /-
 theorem mk_eq_mk_of_basis' {ι' : Type w} (v : Basis ι R M) (v' : Basis ι' R M) : (#ι) = (#ι') :=
   Cardinal.lift_inj.1 <| mk_eq_mk_of_basis v v'
 #align mk_eq_mk_of_basis' mk_eq_mk_of_basis'
+-/
 
 end InvariantBasisNumber
 
@@ -605,6 +791,12 @@ variable {R : Type u} [Ring R] [RankCondition R]
 
 variable {M : Type v} [AddCommGroup M] [Module R M]
 
+/- warning: basis.le_span'' -> Basis.le_span'' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : RankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}} [_inst_5 : Fintype.{u3} ι], (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (forall {w : Set.{u2} M} [_inst_6 : Fintype.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) w)], (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 w) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) -> (LE.le.{0} Nat Nat.hasLe (Fintype.card.{u3} ι _inst_5) (Fintype.card.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) w) _inst_6)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] [_inst_2 : RankCondition.{u2} R (Ring.toSemiring.{u2} R _inst_1)] {M : Type.{u3}} [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] {ι : Type.{u1}} [_inst_5 : Fintype.{u1} ι], (Basis.{u1, u2, u3} ι R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) -> (forall {w : Set.{u3} M} [_inst_6 : Fintype.{u3} (Set.Elem.{u3} M w)], (Eq.{succ u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4 w) (Top.top.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (Submodule.instTopSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4))) -> (LE.le.{0} Nat instLENat (Fintype.card.{u1} ι _inst_5) (Fintype.card.{u3} (Set.Elem.{u3} M w) _inst_6)))
+Case conversion may be inaccurate. Consider using '#align basis.le_span'' Basis.le_span''ₓ'. -/
 /-- An auxiliary lemma for `basis.le_span`.
 
 If `R` satisfies the rank condition,
@@ -625,6 +817,12 @@ theorem Basis.le_span'' {ι : Type _} [Fintype ι] (b : Basis ι R M) {w : Set M
     simpa using s
 #align basis.le_span'' Basis.le_span''
 
+/- warning: basis_le_span' -> basis_le_span' is a dubious translation:
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 /--
 Another auxiliary lemma for `basis.le_span`, which does not require assuming the basis is finite,
 but still assumes we have a finite spanning set.
@@ -639,6 +837,12 @@ theorem basis_le_span' {ι : Type _} (b : Basis ι R M) {w : Set M} [Fintype w]
   exact Basis.le_span'' b s
 #align basis_le_span' basis_le_span'
 
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+Case conversion may be inaccurate. Consider using '#align basis.le_span Basis.le_spanₓ'. -/
 -- Note that if `R` satisfies the strong rank condition,
 -- this also follows from `linear_independent_le_span` below.
 /-- If `R` satisfies the rank condition,
@@ -685,6 +889,12 @@ variable {M : Type v} [AddCommGroup M] [Module R M]
 
 open Submodule
 
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+Case conversion may be inaccurate. Consider using '#align linear_independent_le_span_aux' linearIndependent_le_span_aux'ₓ'. -/
 -- An auxiliary lemma for `linear_independent_le_span'`,
 -- with the additional assumption that the linearly independent family is finite.
 theorem linearIndependent_le_span_aux' {ι : Type _} [Fintype ι] (v : ι → M)
@@ -705,6 +915,7 @@ theorem linearIndependent_le_span_aux' {ι : Type _} [Fintype ι] (v : ι → M)
     exact sub_eq_zero.mp (linear_independent_iff.mp i _ h)
 #align linear_independent_le_span_aux' linearIndependent_le_span_aux'
 
+#print linearIndependentFintypeOfLeSpanFintype /-
 /-- If `R` satisfies the strong rank condition,
 then any linearly independent family `v : ι → M`
 contained in the span of some finite `w : set M`,
@@ -719,7 +930,14 @@ def linearIndependentFintypeOfLeSpanFintype {ι : Type _} (v : ι → M) (i : Li
     have s' : range v' ≤ span R w := (range_comp_subset_range _ _).trans s
     simpa using linearIndependent_le_span_aux' v' i' w s'
 #align linear_independent_fintype_of_le_span_fintype linearIndependentFintypeOfLeSpanFintype
+-/
 
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 /-- If `R` satisfies the strong rank condition,
 then for any linearly independent family `v : ι → M`
 contained in the span of some finite `w : set M`,
@@ -734,6 +952,12 @@ theorem linearIndependent_le_span' {ι : Type _} (v : ι → M) (i : LinearIndep
   exact linearIndependent_le_span_aux' v i w s
 #align linear_independent_le_span' linearIndependent_le_span'
 
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+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] [_inst_2 : StrongRankCondition.{u2} R (Ring.toSemiring.{u2} R _inst_1)] {M : Type.{u3}} [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] {ι : Type.{u1}} (v : ι -> M), (LinearIndependent.{u1, u2, u3} ι R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) -> (forall (w : Set.{u3} M) [_inst_5 : Fintype.{u3} (Set.Elem.{u3} M w)], (Eq.{succ u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (Submodule.span.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4 w) (Top.top.{u3} (Submodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) (Submodule.instTopSubmodule.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4))) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} ι) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} (Fintype.card.{u3} (Set.Elem.{u3} M w) _inst_5))))
+Case conversion may be inaccurate. Consider using '#align linear_independent_le_span linearIndependent_le_spanₓ'. -/
 /-- If `R` satisfies the strong rank condition,
 then for any linearly independent family `v : ι → M`
 and any finite spanning set `w : set M`,
@@ -747,6 +971,12 @@ theorem linearIndependent_le_span {ι : Type _} (v : ι → M) (i : LinearIndepe
   exact le_top
 #align linear_independent_le_span linearIndependent_le_span
 
+/- warning: linear_independent_le_infinite_basis -> linearIndependent_le_infinite_basis is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}}, (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (forall [_inst_5 : Infinite.{succ u3} ι] {κ : Type.{u3}} (v : κ -> M), (LinearIndependent.{u3, u1, u2} κ R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (LE.le.{succ u3} Cardinal.{u3} Cardinal.hasLe.{u3} (Cardinal.mk.{u3} κ) (Cardinal.mk.{u3} ι)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] [_inst_2 : StrongRankCondition.{u2} R (Ring.toSemiring.{u2} R _inst_1)] {M : Type.{u3}} [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] {ι : Type.{u1}}, (Basis.{u1, u2, u3} ι R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) -> (forall [_inst_5 : Infinite.{succ u1} ι] {κ : Type.{u1}} (v : κ -> M), (LinearIndependent.{u1, u2, u3} κ R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} κ) (Cardinal.mk.{u1} ι)))
+Case conversion may be inaccurate. Consider using '#align linear_independent_le_infinite_basis linearIndependent_le_infinite_basisₓ'. -/
 /-- An auxiliary lemma for `linear_independent_le_basis`:
 we handle the case where the basis `b` is infinite.
 -/
@@ -768,6 +998,12 @@ theorem linearIndependent_le_infinite_basis {ι : Type _} (b : Basis ι R M) [In
   exact w.false
 #align linear_independent_le_infinite_basis linearIndependent_le_infinite_basis
 
+/- warning: linear_independent_le_basis -> linearIndependent_le_basis is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}}, (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (forall {κ : Type.{u3}} (v : κ -> M), (LinearIndependent.{u3, u1, u2} κ R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (LE.le.{succ u3} Cardinal.{u3} Cardinal.hasLe.{u3} (Cardinal.mk.{u3} κ) (Cardinal.mk.{u3} ι)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] [_inst_2 : StrongRankCondition.{u2} R (Ring.toSemiring.{u2} R _inst_1)] {M : Type.{u3}} [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] {ι : Type.{u1}}, (Basis.{u1, u2, u3} ι R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) -> (forall {κ : Type.{u1}} (v : κ -> M), (LinearIndependent.{u1, u2, u3} κ R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} κ) (Cardinal.mk.{u1} ι)))
+Case conversion may be inaccurate. Consider using '#align linear_independent_le_basis linearIndependent_le_basisₓ'. -/
 /-- Over any ring `R` satisfying the strong rank condition,
 if `b` is a basis for a module `M`,
 and `s` is a linearly independent set,
@@ -788,12 +1024,20 @@ theorem linearIndependent_le_basis {ι : Type _} (b : Basis ι R M) {κ : Type _
     exact linearIndependent_le_infinite_basis b v i
 #align linear_independent_le_basis linearIndependent_le_basis
 
+#print Basis.card_le_card_of_linearIndependent_aux /-
 /-- In an `n`-dimensional space, the rank is at most `m`. -/
 theorem Basis.card_le_card_of_linearIndependent_aux {R : Type _} [Ring R] [StrongRankCondition R]
     (n : ℕ) {m : ℕ} (v : Fin m → Fin n → R) : LinearIndependent R v → m ≤ n := fun h => by
   simpa using linearIndependent_le_basis (Pi.basisFun R (Fin n)) v h
 #align basis.card_le_card_of_linear_independent_aux Basis.card_le_card_of_linearIndependent_aux
+-/
 
+/- warning: maximal_linear_independent_eq_infinite_basis -> maximal_linearIndependent_eq_infinite_basis is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}}, (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (forall [_inst_5 : Infinite.{succ u3} ι] {κ : Type.{u3}} (v : κ -> M) (i : LinearIndependent.{u3, u1, u2} κ R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), (LinearIndependent.Maximal.{u1, u2, u3} κ R (Ring.toSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 v i) -> (Eq.{succ (succ u3)} Cardinal.{u3} (Cardinal.mk.{u3} κ) (Cardinal.mk.{u3} ι)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] [_inst_2 : StrongRankCondition.{u2} R (Ring.toSemiring.{u2} R _inst_1)] {M : Type.{u3}} [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] {ι : Type.{u1}}, (Basis.{u1, u2, u3} ι R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) -> (forall [_inst_5 : Infinite.{succ u1} ι] {κ : Type.{u1}} (v : κ -> M) (i : LinearIndependent.{u1, u2, u3} κ R M v (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4), (LinearIndependent.Maximal.{u2, u3, u1} κ R (Ring.toSemiring.{u2} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4 v i) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} κ) (Cardinal.mk.{u1} ι)))
+Case conversion may be inaccurate. Consider using '#align maximal_linear_independent_eq_infinite_basis maximal_linearIndependent_eq_infinite_basisₓ'. -/
 -- When the basis is not infinite this need not be true!
 /-- Over any ring `R` satisfying the strong rank condition,
 if `b` is an infinite basis for a module `M`,
@@ -811,6 +1055,7 @@ theorem maximal_linearIndependent_eq_infinite_basis {ι : Type _} (b : Basis ι
     exact infinite_basis_le_maximal_linearIndependent b v i m
 #align maximal_linear_independent_eq_infinite_basis maximal_linearIndependent_eq_infinite_basis
 
+#print Basis.mk_eq_rank'' /-
 theorem Basis.mk_eq_rank'' {ι : Type v} (v : Basis ι R M) : (#ι) = Module.rank R M :=
   by
   haveI := nontrivial_of_invariantBasisNumber R
@@ -829,11 +1074,20 @@ theorem Basis.mk_eq_rank'' {ι : Type v} (v : Basis ι R M) : (#ι) = Module.ran
     rintro ⟨s, li⟩
     apply linearIndependent_le_basis v _ li
 #align basis.mk_eq_rank'' Basis.mk_eq_rank''
+-/
 
+#print Basis.mk_range_eq_rank /-
 theorem Basis.mk_range_eq_rank (v : Basis ι R M) : (#range v) = Module.rank R M :=
   v.reindexRange.mk_eq_rank''
 #align basis.mk_range_eq_rank Basis.mk_range_eq_rank
+-/
 
+/- warning: rank_eq_card_basis -> rank_eq_card_basis is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}} [_inst_5 : Fintype.{u3} ι], (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) ((fun (a : Type) (b : Type.{succ u2}) [self : HasLiftT.{1, succ (succ u2)} a b] => self.0) Nat Cardinal.{u2} (HasLiftT.mk.{1, succ (succ u2)} Nat Cardinal.{u2} (CoeTCₓ.coe.{1, succ (succ u2)} Nat Cardinal.{u2} (Nat.castCoe.{succ u2} Cardinal.{u2} Cardinal.hasNatCast.{u2}))) (Fintype.card.{u3} ι _inst_5)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}} [_inst_5 : Fintype.{u3} ι], (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Nat.cast.{succ u2} Cardinal.{u2} Cardinal.instNatCastCardinal.{u2} (Fintype.card.{u3} ι _inst_5)))
+Case conversion may be inaccurate. Consider using '#align rank_eq_card_basis rank_eq_card_basisₓ'. -/
 /-- If a vector space has a finite basis, then its dimension (seen as a cardinal) is equal to the
 cardinality of the basis. -/
 theorem rank_eq_card_basis {ι : Type w} [Fintype ι] (h : Basis ι R M) :
@@ -843,38 +1097,62 @@ theorem rank_eq_card_basis {ι : Type w} [Fintype ι] (h : Basis ι R M) :
   rw [← h.mk_range_eq_rank, Cardinal.mk_fintype, Set.card_range_of_injective h.injective]
 #align rank_eq_card_basis rank_eq_card_basis
 
+/- warning: basis.card_le_card_of_linear_independent -> Basis.card_le_card_of_linearIndependent is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}} [_inst_5 : Fintype.{u3} ι], (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (forall {ι' : Type.{u4}} [_inst_6 : Fintype.{u4} ι'] {v : ι' -> M}, (LinearIndependent.{u4, u1, u2} ι' R M v (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (LE.le.{0} Nat Nat.hasLe (Fintype.card.{u4} ι' _inst_6) (Fintype.card.{u3} ι _inst_5)))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : Ring.{u3} R] [_inst_2 : StrongRankCondition.{u3} R (Ring.toSemiring.{u3} R _inst_1)] {M : Type.{u4}} [_inst_3 : AddCommGroup.{u4} M] [_inst_4 : Module.{u3, u4} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_3)] {ι : Type.{u2}} [_inst_5 : Fintype.{u2} ι], (Basis.{u2, u3, u4} ι R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) -> (forall {ι' : Type.{u1}} [_inst_6 : Fintype.{u1} ι'] {v : ι' -> M}, (LinearIndependent.{u1, u3, u4} ι' R M v (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} M _inst_3) _inst_4) -> (LE.le.{0} Nat instLENat (Fintype.card.{u1} ι' _inst_6) (Fintype.card.{u2} ι _inst_5)))
+Case conversion may be inaccurate. Consider using '#align basis.card_le_card_of_linear_independent Basis.card_le_card_of_linearIndependentₓ'. -/
 theorem Basis.card_le_card_of_linearIndependent {ι : Type _} [Fintype ι] (b : Basis ι R M)
     {ι' : Type _} [Fintype ι'] {v : ι' → M} (hv : LinearIndependent R v) :
     Fintype.card ι' ≤ Fintype.card ι :=
   by
   letI := nontrivial_of_invariantBasisNumber R
   simpa [rank_eq_card_basis b, Cardinal.mk_fintype] using
-    cardinal_lift_le_rank_of_linear_independent' hv
+    cardinal_lift_le_rank_of_linearIndependent' hv
 #align basis.card_le_card_of_linear_independent Basis.card_le_card_of_linearIndependent
 
+#print Basis.card_le_card_of_submodule /-
 theorem Basis.card_le_card_of_submodule (N : Submodule R M) [Fintype ι] (b : Basis ι R M)
     [Fintype ι'] (b' : Basis ι' R N) : Fintype.card ι' ≤ Fintype.card ι :=
   b.card_le_card_of_linearIndependent (b'.LinearIndependent.map' N.Subtype N.ker_subtype)
 #align basis.card_le_card_of_submodule Basis.card_le_card_of_submodule
+-/
 
+/- warning: basis.card_le_card_of_le -> Basis.card_le_card_of_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u3}} {ι' : Type.{u4}} {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4} {O : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4}, (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) N O) -> (forall [_inst_5 : Fintype.{u3} ι], (Basis.{u3, u1, u2} ι R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) O) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 O) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 O)) -> (forall [_inst_6 : Fintype.{u4} ι'], (Basis.{u4, u1, u2} ι' R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) N) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 N) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 N)) -> (LE.le.{0} Nat Nat.hasLe (Fintype.card.{u4} ι' _inst_6) (Fintype.card.{u3} ι _inst_5))))
+but is expected to have type
+  forall {ι : Type.{u3}} {ι' : Type.{u4}} {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4} {O : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4}, (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) N O) -> (forall [_inst_5 : Fintype.{u3} ι], (Basis.{u3, u1, u2} ι R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) x O)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 O) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 O)) -> (forall [_inst_6 : Fintype.{u4} ι'], (Basis.{u4, u1, u2} ι' R (Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) x N)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 N) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 N)) -> (LE.le.{0} Nat instLENat (Fintype.card.{u4} ι' _inst_6) (Fintype.card.{u3} ι _inst_5))))
+Case conversion may be inaccurate. Consider using '#align basis.card_le_card_of_le Basis.card_le_card_of_leₓ'. -/
 theorem Basis.card_le_card_of_le {N O : Submodule R M} (hNO : N ≤ O) [Fintype ι] (b : Basis ι R O)
     [Fintype ι'] (b' : Basis ι' R N) : Fintype.card ι' ≤ Fintype.card ι :=
   b.card_le_card_of_linearIndependent
     (b'.LinearIndependent.map' (Submodule.ofLe hNO) (N.ker_ofLe O _))
 #align basis.card_le_card_of_le Basis.card_le_card_of_le
 
+#print Basis.mk_eq_rank /-
 theorem Basis.mk_eq_rank (v : Basis ι R M) :
     Cardinal.lift.{v} (#ι) = Cardinal.lift.{w} (Module.rank R M) :=
   by
   haveI := nontrivial_of_invariantBasisNumber R
   rw [← v.mk_range_eq_rank, Cardinal.mk_range_eq_of_injective v.injective]
 #align basis.mk_eq_rank Basis.mk_eq_rank
+-/
 
+#print Basis.mk_eq_rank' /-
 theorem Basis.mk_eq_rank'.{m} (v : Basis ι R M) :
     Cardinal.lift.{max v m} (#ι) = Cardinal.lift.{max w m} (Module.rank R M) := by
   simpa using v.mk_eq_rank
 #align basis.mk_eq_rank' Basis.mk_eq_rank'
+-/
 
+/- warning: basis.nonempty_fintype_index_of_rank_lt_aleph_0 -> Basis.nonempty_fintype_index_of_rank_lt_aleph0 is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}}, (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} (OrderedAddCommMonoid.toPartialOrder.{succ u2} Cardinal.{u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ u2} Cardinal.{u2} (OrderedCommSemiring.toOrderedSemiring.{succ u2} Cardinal.{u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u2} Cardinal.{u2} Cardinal.canonicallyOrderedCommSemiring.{u2})))))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Cardinal.aleph0.{u2}) -> (Nonempty.{succ u3} (Fintype.{u3} ι))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] [_inst_2 : StrongRankCondition.{u2} R (Ring.toSemiring.{u2} R _inst_1)] {M : Type.{u3}} [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] {ι : Type.{u1}}, (Basis.{u1, u2, u3} ι R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) -> (LT.lt.{succ u3} Cardinal.{u3} (Preorder.toLT.{succ u3} Cardinal.{u3} (PartialOrder.toPreorder.{succ u3} Cardinal.{u3} Cardinal.partialOrder.{u3})) (Module.rank.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) Cardinal.aleph0.{u3}) -> (Nonempty.{succ u1} (Fintype.{u1} ι))
+Case conversion may be inaccurate. Consider using '#align basis.nonempty_fintype_index_of_rank_lt_aleph_0 Basis.nonempty_fintype_index_of_rank_lt_aleph0ₓ'. -/
 /-- If a module has a finite dimension, all bases are indexed by a finite type. -/
 theorem Basis.nonempty_fintype_index_of_rank_lt_aleph0 {ι : Type _} (b : Basis ι R M)
     (h : Module.rank R M < ℵ₀) : Nonempty (Fintype ι) := by
@@ -882,18 +1160,27 @@ theorem Basis.nonempty_fintype_index_of_rank_lt_aleph0 {ι : Type _} (b : Basis
     Cardinal.lt_aleph0_iff_fintype] at h
 #align basis.nonempty_fintype_index_of_rank_lt_aleph_0 Basis.nonempty_fintype_index_of_rank_lt_aleph0
 
+#print Basis.fintypeIndexOfRankLtAleph0 /-
 /-- If a module has a finite dimension, all bases are indexed by a finite type. -/
 noncomputable def Basis.fintypeIndexOfRankLtAleph0 {ι : Type _} (b : Basis ι R M)
     (h : Module.rank R M < ℵ₀) : Fintype ι :=
   Classical.choice (b.nonempty_fintype_index_of_rank_lt_aleph0 h)
 #align basis.fintype_index_of_rank_lt_aleph_0 Basis.fintypeIndexOfRankLtAleph0
+-/
 
+/- warning: basis.finite_index_of_rank_lt_aleph_0 -> Basis.finite_index_of_rank_lt_aleph0 is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {ι : Type.{u3}} {s : Set.{u3} ι}, (Basis.{u3, u1, u2} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} (OrderedAddCommMonoid.toPartialOrder.{succ u2} Cardinal.{u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ u2} Cardinal.{u2} (OrderedCommSemiring.toOrderedSemiring.{succ u2} Cardinal.{u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u2} Cardinal.{u2} Cardinal.canonicallyOrderedCommSemiring.{u2})))))) (Module.rank.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) Cardinal.aleph0.{u2}) -> (Set.Finite.{u3} ι s)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : Ring.{u2} R] [_inst_2 : StrongRankCondition.{u2} R (Ring.toSemiring.{u2} R _inst_1)] {M : Type.{u3}} [_inst_3 : AddCommGroup.{u3} M] [_inst_4 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3)] {ι : Type.{u1}} {s : Set.{u1} ι}, (Basis.{u1, u2, u3} (Set.Elem.{u1} ι s) R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) -> (LT.lt.{succ u3} Cardinal.{u3} (Preorder.toLT.{succ u3} Cardinal.{u3} (PartialOrder.toPreorder.{succ u3} Cardinal.{u3} Cardinal.partialOrder.{u3})) (Module.rank.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_3) _inst_4) Cardinal.aleph0.{u3}) -> (Set.Finite.{u1} ι s)
+Case conversion may be inaccurate. Consider using '#align basis.finite_index_of_rank_lt_aleph_0 Basis.finite_index_of_rank_lt_aleph0ₓ'. -/
 /-- If a module has a finite dimension, all bases are indexed by a finite set. -/
 theorem Basis.finite_index_of_rank_lt_aleph0 {ι : Type _} {s : Set ι} (b : Basis s R M)
     (h : Module.rank R M < ℵ₀) : s.Finite :=
   finite_def.2 (b.nonempty_fintype_index_of_rank_lt_aleph0 h)
 #align basis.finite_index_of_rank_lt_aleph_0 Basis.finite_index_of_rank_lt_aleph0
 
+#print rank_span /-
 theorem rank_span {v : ι → M} (hv : LinearIndependent R v) :
     Module.rank R ↥(span R (range v)) = (#range v) :=
   by
@@ -901,14 +1188,23 @@ theorem rank_span {v : ι → M} (hv : LinearIndependent R v) :
   rw [← Cardinal.lift_inj, ← (Basis.span hv).mk_eq_rank,
     Cardinal.mk_range_eq_of_injective (@LinearIndependent.injective ι R M v _ _ _ _ hv)]
 #align rank_span rank_span
+-/
 
+#print rank_span_set /-
 theorem rank_span_set {s : Set M} (hs : LinearIndependent R (fun x => x : s → M)) :
     Module.rank R ↥(span R s) = (#s) :=
   by
   rw [← @set_of_mem_eq _ s, ← Subtype.range_coe_subtype]
   exact rank_span hs
 #align rank_span_set rank_span_set
+-/
 
+/- warning: submodule.induction_on_rank -> Submodule.inductionOnRank is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u3}} {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_5 : IsDomain.{u1} R (Ring.toSemiring.{u1} R _inst_1)] [_inst_6 : Fintype.{u3} ι], (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (forall (P : (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> Sort.{u4}), (forall (N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), (forall (N' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) N' N) -> (forall (x : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) x N) -> (forall (c : R) (y : M), (Membership.Mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) y N') -> (Eq.{succ u2} M (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_3)))))) (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_3)))) (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_3)))) (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_3)))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) c x) y) (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_3))))))))) -> (Eq.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)))))))))) -> (P N'))) -> (P N)) -> (forall (N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), P N))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u1}} [_inst_1 : Ring.{u1} R] [_inst_2 : StrongRankCondition.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {M : Type.{u2}} [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_5 : IsDomain.{u1} R (Ring.toSemiring.{u1} R _inst_1)] [_inst_6 : Fintype.{u3} ι], (Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> (forall (P : (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) -> Sort.{u4}), (forall (N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), (forall (N' : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), (LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) N' N) -> (forall (x : M), (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) x N) -> (forall (c : R) (y : M), (Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) y N') -> (Eq.{succ u2} M (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_3)))))) (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_3))))) (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_3))))) (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_3))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) c x) y) (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_3)))))))) -> (Eq.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) -> (P N'))) -> (P N)) -> (forall (N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), P N))
+Case conversion may be inaccurate. Consider using '#align submodule.induction_on_rank Submodule.inductionOnRankₓ'. -/
 /-- If `N` is a submodule in a free, finitely generated module,
 do induction on adjoining a linear independent element to a submodule. -/
 def Submodule.inductionOnRank [IsDomain R] [Fintype ι] (b : Basis ι R M)
@@ -921,6 +1217,12 @@ def Submodule.inductionOnRank [IsDomain R] [Fintype ι] (b : Basis ι R M)
     simpa using b.card_le_card_of_linear_independent hli
 #align submodule.induction_on_rank Submodule.inductionOnRank
 
+/- warning: ideal.rank_eq -> Ideal.rank_eq 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 ideal.rank_eq Ideal.rank_eqₓ'. -/
 /-- If `S` a finite-dimensional ring extension of `R` which is free as an `R`-module,
 then the rank of an ideal `I` of `S` over `R` is the same as the rank of `S`.
 -/
@@ -947,10 +1249,12 @@ theorem Ideal.rank_eq {R S : Type _} [CommRing R] [StrongRankCondition R] [Ring
 
 variable (R)
 
+#print rank_self /-
 @[simp]
 theorem rank_self : Module.rank R R = 1 := by
   rw [← Cardinal.lift_inj, ← (Basis.singleton PUnit R).mk_eq_rank, Cardinal.mk_pUnit]
 #align rank_self rank_self
+-/
 
 end StrongRankCondition
 
@@ -970,10 +1274,12 @@ namespace Module.Free
 
 variable (K V)
 
+#print Module.Free.rank_eq_card_chooseBasisIndex /-
 /-- The rank of a free module `M` over `R` is the cardinality of `choose_basis_index R M`. -/
 theorem rank_eq_card_chooseBasisIndex : Module.rank K V = (#ChooseBasisIndex K V) :=
   (chooseBasis K V).mk_eq_rank''.symm
 #align module.free.rank_eq_card_choose_basis_index Module.Free.rank_eq_card_chooseBasisIndex
+-/
 
 end Module.Free
 
@@ -981,6 +1287,7 @@ open Module.Free
 
 open Cardinal
 
+#print nonempty_linearEquiv_of_lift_rank_eq /-
 /-- Two vector spaces are isomorphic if they have the same dimension. -/
 theorem nonempty_linearEquiv_of_lift_rank_eq
     (cond : Cardinal.lift.{v'} (Module.rank K V) = Cardinal.lift.{v} (Module.rank K V')) :
@@ -992,44 +1299,61 @@ theorem nonempty_linearEquiv_of_lift_rank_eq
     rw [B.mk_eq_rank'', cond, B'.mk_eq_rank'']
   exact (Cardinal.lift_mk_eq.{v, v', 0}.1 this).map (B.equiv B')
 #align nonempty_linear_equiv_of_lift_rank_eq nonempty_linearEquiv_of_lift_rank_eq
+-/
 
+#print nonempty_linearEquiv_of_rank_eq /-
 /-- Two vector spaces are isomorphic if they have the same dimension. -/
 theorem nonempty_linearEquiv_of_rank_eq (cond : Module.rank K V = Module.rank K V₁) :
     Nonempty (V ≃ₗ[K] V₁) :=
   nonempty_linearEquiv_of_lift_rank_eq <| congr_arg _ cond
 #align nonempty_linear_equiv_of_rank_eq nonempty_linearEquiv_of_rank_eq
+-/
 
 section
 
 variable (V V' V₁)
 
+#print LinearEquiv.ofLiftRankEq /-
 /-- Two vector spaces are isomorphic if they have the same dimension. -/
 def LinearEquiv.ofLiftRankEq
     (cond : Cardinal.lift.{v'} (Module.rank K V) = Cardinal.lift.{v} (Module.rank K V')) :
     V ≃ₗ[K] V' :=
   Classical.choice (nonempty_linearEquiv_of_lift_rank_eq cond)
 #align linear_equiv.of_lift_rank_eq LinearEquiv.ofLiftRankEq
+-/
 
+#print LinearEquiv.ofRankEq /-
 /-- Two vector spaces are isomorphic if they have the same dimension. -/
 def LinearEquiv.ofRankEq (cond : Module.rank K V = Module.rank K V₁) : V ≃ₗ[K] V₁ :=
   Classical.choice (nonempty_linearEquiv_of_rank_eq cond)
 #align linear_equiv.of_rank_eq LinearEquiv.ofRankEq
+-/
 
 end
 
+#print LinearEquiv.nonempty_equiv_iff_lift_rank_eq /-
 /-- Two vector spaces are isomorphic if and only if they have the same dimension. -/
 theorem LinearEquiv.nonempty_equiv_iff_lift_rank_eq :
     Nonempty (V ≃ₗ[K] V') ↔
       Cardinal.lift.{v'} (Module.rank K V) = Cardinal.lift.{v} (Module.rank K V') :=
   ⟨fun ⟨h⟩ => LinearEquiv.lift_rank_eq h, fun h => nonempty_linearEquiv_of_lift_rank_eq h⟩
 #align linear_equiv.nonempty_equiv_iff_lift_rank_eq LinearEquiv.nonempty_equiv_iff_lift_rank_eq
+-/
 
+#print LinearEquiv.nonempty_equiv_iff_rank_eq /-
 /-- Two vector spaces are isomorphic if and only if they have the same dimension. -/
 theorem LinearEquiv.nonempty_equiv_iff_rank_eq :
     Nonempty (V ≃ₗ[K] V₁) ↔ Module.rank K V = Module.rank K V₁ :=
   ⟨fun ⟨h⟩ => LinearEquiv.rank_eq h, fun h => nonempty_linearEquiv_of_rank_eq h⟩
 #align linear_equiv.nonempty_equiv_iff_rank_eq LinearEquiv.nonempty_equiv_iff_rank_eq
+-/
 
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 /-- The rank of `M × N` is `(module.rank R M).lift + (module.rank R N).lift`. -/
 @[simp]
 theorem rank_prod :
@@ -1040,6 +1364,12 @@ theorem rank_prod :
     lift_umax'] using ((choose_basis K V).Prod (choose_basis K V')).mk_eq_rank.symm
 #align rank_prod rank_prod
 
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+Case conversion may be inaccurate. Consider using '#align rank_prod' rank_prod'ₓ'. -/
 /-- If `M` and `N` lie in the same universe, the rank of `M × N` is
   `(module.rank R M) + (module.rank R N)`. -/
 theorem rank_prod' : Module.rank K (V × V₁) = Module.rank K V + Module.rank K V₁ := by simp
@@ -1051,6 +1381,12 @@ variable [∀ i, AddCommGroup (φ i)] [∀ i, Module K (φ i)] [∀ i, Module.Fr
 
 open LinearMap
 
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 /-- The rank of a finite product is the sum of the ranks. -/
 @[simp]
 theorem rank_pi [Finite η] : Module.rank K (∀ i, φ i) = Cardinal.sum fun i => Module.rank K (φ i) :=
@@ -1063,26 +1399,56 @@ theorem rank_pi [Finite η] : Module.rank K (∀ i, φ i) = Cardinal.sum fun i =
 
 variable [Fintype η]
 
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 theorem rank_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] [Module.Free K V] :
     Module.rank K (η → V) = Fintype.card η * Module.rank K V := by
   rw [rank_pi, Cardinal.sum_const', Cardinal.mk_fintype]
 #align rank_fun rank_fun
 
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 theorem rank_fun_eq_lift_mul :
     Module.rank K (η → V) =
       (Fintype.card η : Cardinal.{max u₁' v}) * Cardinal.lift.{u₁'} (Module.rank K V) :=
   by rw [rank_pi, Cardinal.sum_const, Cardinal.mk_fintype, Cardinal.lift_natCast]
 #align rank_fun_eq_lift_mul rank_fun_eq_lift_mul
 
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 theorem rank_fun' : Module.rank K (η → K) = Fintype.card η := by
   rw [rank_fun_eq_lift_mul, rank_self, Cardinal.lift_one, mul_one, Cardinal.natCast_inj]
 #align rank_fun' rank_fun'
 
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+Case conversion may be inaccurate. Consider using '#align rank_fin_fun rank_fin_funₓ'. -/
 theorem rank_fin_fun (n : ℕ) : Module.rank K (Fin n → K) = n := by simp [rank_fun']
 #align rank_fin_fun rank_fin_fun
 
 end Fintype
 
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+Case conversion may be inaccurate. Consider using '#align fin_dim_vectorspace_equiv finDimVectorspaceEquivₓ'. -/
 -- TODO: merge with the `finrank` content
 /-- An `n`-dimensional `K`-vector space is equivalent to `fin n → K`. -/
 def finDimVectorspaceEquiv (n : ℕ) (hn : Module.rank K V = n) : V ≃ₗ[K] Fin n → K :=
@@ -1110,12 +1476,15 @@ variable [AddCommGroup V₁] [Module K V₁]
 
 variable {K V}
 
+#print Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0 /-
 /-- If a vector space has a finite dimension, the index set of `basis.of_vector_space` is finite. -/
 theorem Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0 (h : Module.rank K V < ℵ₀) :
     (Basis.ofVectorSpaceIndex K V).Finite :=
   finite_def.2 <| (Basis.ofVectorSpace K V).nonempty_fintype_index_of_rank_lt_aleph0 h
 #align basis.finite_of_vector_space_index_of_rank_lt_aleph_0 Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0
+-/
 
+#print rank_span_le /-
 -- TODO how far can we generalise this?
 -- When `s` is finite, we could prove this for any ring satisfying the strong rank condition
 -- using `linear_independent_le_span'`
@@ -1125,7 +1494,9 @@ theorem rank_span_le (s : Set V) : Module.rank K (span K s) ≤ (#s) :=
   convert Cardinal.mk_le_mk_of_subset hb
   rw [← hsab, rank_span_set hlib]
 #align rank_span_le rank_span_le
+-/
 
+#print rank_span_of_finset /-
 theorem rank_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V)) < ℵ₀ :=
   calc
     Module.rank K (span K (↑s : Set V)) ≤ (#(↑s : Set V)) := rank_span_le ↑s
@@ -1133,7 +1504,14 @@ theorem rank_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V
     _ < ℵ₀ := Cardinal.nat_lt_aleph0 _
     
 #align rank_span_of_finset rank_span_of_finset
+-/
 
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 theorem rank_quotient_add_rank (p : Submodule K V) :
     Module.rank K (V ⧸ p) + Module.rank K p = Module.rank K V := by
   classical exact
@@ -1141,6 +1519,12 @@ theorem rank_quotient_add_rank (p : Submodule K V) :
       rank_prod'.symm.trans f.rank_eq
 #align rank_quotient_add_rank rank_quotient_add_rank
 
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(LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)))) (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)
+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7), Eq.{succ (succ u2)} Cardinal.{u2} (HAdd.hAdd.{succ u2, succ u2, 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+Case conversion may be inaccurate. Consider using '#align rank_range_add_rank_ker rank_range_add_rank_kerₓ'. -/
 /-- rank-nullity theorem -/
 theorem rank_range_add_rank_ker (f : V →ₗ[K] V₁) :
     Module.rank K f.range + Module.rank K f.ker = Module.rank K V :=
@@ -1149,6 +1533,12 @@ theorem rank_range_add_rank_ker (f : V →ₗ[K] V₁) :
   rw [← f.quot_ker_equiv_range.rank_eq, rank_quotient_add_rank]
 #align rank_range_add_rank_ker rank_range_add_rank_ker
 
+/- warning: rank_eq_of_surjective -> rank_eq_of_surjective is a dubious translation:
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+  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] (f : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7), (Function.Surjective.{succ u2, succ u2} V V₁ (FunLike.coe.{succ 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(DivisionRing.toRing.{u1} K _inst_1))))) f)) -> (Eq.{succ (succ u2)} Cardinal.{u2} (Module.rank.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Module.rank.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f))) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)) (Submodule.module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (LinearMap.ker.{u1, u1, u2, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V₁ (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} K K V V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f)))))
+Case conversion may be inaccurate. Consider using '#align rank_eq_of_surjective rank_eq_of_surjectiveₓ'. -/
 theorem rank_eq_of_surjective (f : V →ₗ[K] V₁) (h : Surjective f) :
     Module.rank K V = Module.rank K V₁ + Module.rank K f.ker := by
   rw [← rank_range_add_rank_ker f, ← rank_range_of_surjective f h]
@@ -1162,6 +1552,12 @@ variable [AddCommGroup V₃] [Module K V₃]
 
 open LinearMap
 
+/- warning: rank_add_rank_split -> rank_add_rank_split is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} {V₂ : Type.{u2}} {V₃ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] [_inst_8 : AddCommGroup.{u2} V₂] [_inst_9 : Module.{u1, u2} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8)] [_inst_10 : AddCommGroup.{u2} V₃] [_inst_11 : Module.{u1, u2} K V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10)] (db : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (eb : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (cd : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (ce : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11), (LE.le.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Top.top.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _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 _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 _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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) db) (LinearMap.range.{u1, u1, u2, u2, u2} K K V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} K K V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) (RingHomSurjective.ids.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))) eb))) -> (Eq.{succ u2} (Submodule.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (LinearMap.ker.{u1, u1, u2, u2, u2} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K 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(Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) db cd) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHomCompTriple.right_ids.{u1, u1} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) eb ce)) -> (forall (d : V₂) (e : V₃), (Eq.{succ u2} V (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) => V₂ -> V) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₂ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) db d) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) => V₃ -> V) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₃ V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) eb e)) -> (Exists.{succ u2} V₁ (fun (c : V₁) => And (Eq.{succ u2} V₂ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) => V₁ -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₁ V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) cd c) d) (Eq.{succ u2} V₃ (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11) (fun (_x : LinearMap.{u1, u1, u2, u2} K K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11) => V₁ -> V₃) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} K K V₁ V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11 (RingHom.id.{u1} K (Semiring.toNonAssocSemiring.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) ce c) e)))) -> (Eq.{succ (succ u2)} Cardinal.{u2} (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Module.rank.{u1, u2} K V₁ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7)) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K V₂ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_9) (Module.rank.{u1, u2} K V₃ (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_11)))
+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} {V₁ : Type.{u2}} {V₂ : Type.{u2}} {V₃ : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u2} V₁] [_inst_7 : Module.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6)] [_inst_8 : AddCommGroup.{u2} V₂] [_inst_9 : Module.{u1, u2} K V₂ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8)] [_inst_10 : AddCommGroup.{u2} V₃] [_inst_11 : Module.{u1, u2} K V₃ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10)] (db : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₂ V (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_9 _inst_3) (eb : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₃ V (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_11 _inst_3) (cd : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_8) _inst_7 _inst_9) (ce : LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V₃ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_7 _inst_11), (LE.le.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} K V 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(RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) cd) (Bot.bot.{u2} (Submodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7) (Submodule.instBotSubmodule.{u1, u2} K V₁ (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) _inst_7))) -> (Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V₁ V (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_3) (LinearMap.comp.{u1, u1, u1, u2, u2, 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(DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) db cd) (LinearMap.comp.{u1, u1, u1, u2, u2, u2} K K K V₁ V₃ V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_6) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_7 _inst_11 _inst_3 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K 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(AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_10) _inst_11)))
+Case conversion may be inaccurate. Consider using '#align rank_add_rank_split rank_add_rank_splitₓ'. -/
 /-- This is mostly an auxiliary lemma for `submodule.rank_sup_add_rank_inf_eq`. -/
 theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd : V₁ →ₗ[K] V₂)
     (ce : V₁ →ₗ[K] V₃) (hde : ⊤ ≤ db.range ⊔ eb.range) (hgd : ker cd = ⊥)
@@ -1193,6 +1589,12 @@ theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd
     rw [h₂, _root_.neg_neg]
 #align rank_add_rank_split rank_add_rank_split
 
+/- warning: submodule.rank_sup_add_rank_inf_eq -> Submodule.rank_sup_add_rank_inf_eq is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (s : Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (t : Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Eq.{succ (succ u2)} Cardinal.{u2} (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _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 _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 _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 _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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) s t)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _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 _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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) s t)) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _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 _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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) s t))) (Module.rank.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (Inf.inf.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) s t)) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Inf.inf.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) s t)) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Inf.inf.{u2} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) s t)))) (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.hasAdd.{u2}) (Module.rank.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) s) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 s) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 s)) (Module.rank.{u1, u2} K (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{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 _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 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) t) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (Submodule.addCommMonoid.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 t) (Submodule.module.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 t)))
+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] (s : Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (t : Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Eq.{succ (succ u2)} Cardinal.{u2} (HAdd.hAdd.{succ u2, succ u2, succ u2} Cardinal.{u2} Cardinal.{u2} Cardinal.{u2} (instHAdd.{succ u2} Cardinal.{u2} Cardinal.instAddCardinal.{u2}) (Module.rank.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (Sup.sup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) 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_inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K 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(AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) s t))) (Module.rank.{u1, u2} K (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K 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+Case conversion may be inaccurate. Consider using '#align submodule.rank_sup_add_rank_inf_eq Submodule.rank_sup_add_rank_inf_eqₓ'. -/
 theorem Submodule.rank_sup_add_rank_inf_eq (s t : Submodule K V) :
     Module.rank K (s ⊔ t : Submodule K V) + Module.rank K (s ⊓ t : Submodule K V) =
       Module.rank K s + Module.rank K t :=
@@ -1209,6 +1611,12 @@ theorem Submodule.rank_sup_add_rank_inf_eq (s t : Submodule K V) :
       exact ⟨⟨b₁, hb₁, hb₂⟩, rfl, rfl⟩)
 #align submodule.rank_sup_add_rank_inf_eq Submodule.rank_sup_add_rank_inf_eq
 
+/- warning: submodule.rank_add_le_rank_add_rank -> Submodule.rank_add_le_rank_add_rank is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align submodule.rank_add_le_rank_add_rank Submodule.rank_add_le_rank_add_rankₓ'. -/
 theorem Submodule.rank_add_le_rank_add_rank (s t : Submodule K V) :
     Module.rank K (s ⊔ t : Submodule K V) ≤ Module.rank K s + Module.rank K t :=
   by
@@ -1226,6 +1634,7 @@ variable [DivisionRing K] [AddCommGroup V] [Module K V] [AddCommGroup V₁] [Mod
 
 variable [AddCommGroup V'] [Module K V']
 
+#print Basis.ofRankEqZero /-
 /-- The `ι` indexed basis on `V`, where `ι` is an empty type and `V` is zero-dimensional.
 
 See also `finite_dimensional.fin_basis`.
@@ -1234,13 +1643,21 @@ def Basis.ofRankEqZero {ι : Type _} [IsEmpty ι] (hV : Module.rank K V = 0) : B
   haveI : Subsingleton V := rank_zero_iff.1 hV
   Basis.empty _
 #align basis.of_rank_eq_zero Basis.ofRankEqZero
+-/
 
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 @[simp]
 theorem Basis.ofRankEqZero_apply {ι : Type _} [IsEmpty ι] (hV : Module.rank K V = 0) (i : ι) :
     Basis.ofRankEqZero hV i = 0 :=
   rfl
 #align basis.of_rank_eq_zero_apply Basis.ofRankEqZero_apply
 
+#print le_rank_iff_exists_linearIndependent /-
 theorem le_rank_iff_exists_linearIndependent {c : Cardinal} :
     c ≤ Module.rank K V ↔ ∃ s : Set V, (#s) = c ∧ LinearIndependent K (coe : s → V) :=
   by
@@ -1253,7 +1670,14 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} :
   · rintro ⟨s, rfl, si⟩
     exact cardinal_le_rank_of_linearIndependent si
 #align le_rank_iff_exists_linear_independent le_rank_iff_exists_linearIndependent
+-/
 
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 theorem le_rank_iff_exists_linearIndependent_finset {n : ℕ} :
     ↑n ≤ Module.rank K V ↔
       ∃ s : Finset V, s.card = n ∧ LinearIndependent K (coe : (s : Set V) → V) :=
@@ -1266,6 +1690,7 @@ theorem le_rank_iff_exists_linearIndependent_finset {n : ℕ} :
     exact ⟨s, ⟨s, rfl, rfl⟩, si⟩
 #align le_rank_iff_exists_linear_independent_finset le_rank_iff_exists_linearIndependent_finset
 
+#print rank_le_one_iff /-
 /-- A vector space has dimension at most `1` if and only if there is a
 single vector of which all vectors are multiples. -/
 theorem rank_le_one_iff : Module.rank K V ≤ 1 ↔ ∃ v₀ : V, ∀ v, ∃ r : K, r • v₀ = v :=
@@ -1292,7 +1717,14 @@ theorem rank_le_one_iff : Module.rank K V ≤ 1 ↔ ∃ v₀ : V, ∀ v, ∃ r :
     refine' (rank_span_le _).trans_eq _
     simp
 #align rank_le_one_iff rank_le_one_iff
+-/
 
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+Case conversion may be inaccurate. Consider using '#align rank_submodule_le_one_iff rank_submodule_le_one_iffₓ'. -/
 /-- A submodule has dimension at most `1` if and only if there is a
 single vector in the submodule such that the submodule is contained in
 its span. -/
@@ -1317,6 +1749,12 @@ theorem rank_submodule_le_one_iff (s : Submodule K V) :
     exact hr
 #align rank_submodule_le_one_iff rank_submodule_le_one_iff
 
+/- warning: rank_submodule_le_one_iff' -> rank_submodule_le_one_iff' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align rank_submodule_le_one_iff' rank_submodule_le_one_iff'ₓ'. -/
 /-- A submodule has dimension at most `1` if and only if there is a
 single vector, not necessarily in the submodule, such that the
 submodule is contained in its span. -/
@@ -1340,6 +1778,7 @@ theorem rank_submodule_le_one_iff' (s : Submodule K V) : Module.rank K s ≤ 1 
       simp [hw]
 #align rank_submodule_le_one_iff' rank_submodule_le_one_iff'
 
+#print Submodule.rank_le_one_iff_isPrincipal /-
 theorem Submodule.rank_le_one_iff_isPrincipal (W : Submodule K V) :
     Module.rank K W ≤ 1 ↔ W.IsPrincipal :=
   by
@@ -1353,7 +1792,14 @@ theorem Submodule.rank_le_one_iff_isPrincipal (W : Submodule K V) :
     choose f hf using h
     exact ⟨⟨a, ha⟩, fun v => ⟨f v.1 v.2, Subtype.ext (hf v.1 v.2)⟩⟩
 #align submodule.rank_le_one_iff_is_principal Submodule.rank_le_one_iff_isPrincipal
+-/
 
+/- warning: module.rank_le_one_iff_top_is_principal -> Module.rank_le_one_iff_top_isPrincipal is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align module.rank_le_one_iff_top_is_principal Module.rank_le_one_iff_top_isPrincipalₓ'. -/
 theorem Module.rank_le_one_iff_top_isPrincipal :
     Module.rank K V ≤ 1 ↔ (⊤ : Submodule K V).IsPrincipal := by
   rw [← Submodule.rank_le_one_iff_isPrincipal, rank_top]
@@ -1374,19 +1820,31 @@ variable [Ring K] [AddCommGroup V] [Module K V] [AddCommGroup V₁] [Module K V
 
 variable [AddCommGroup V'] [Module K V']
 
+#print LinearMap.rank /-
 /-- `rank f` is the rank of a `linear_map` `f`, defined as the dimension of `f.range`. -/
 def rank (f : V →ₗ[K] V') : Cardinal :=
   Module.rank K f.range
 #align linear_map.rank LinearMap.rank
+-/
 
+#print LinearMap.rank_le_range /-
 theorem rank_le_range (f : V →ₗ[K] V') : rank f ≤ Module.rank K V' :=
   rank_submodule_le _
 #align linear_map.rank_le_range LinearMap.rank_le_range
+-/
 
+#print LinearMap.rank_le_domain /-
 theorem rank_le_domain (f : V →ₗ[K] V₁) : rank f ≤ Module.rank K V :=
   rank_range_le _
 #align linear_map.rank_le_domain LinearMap.rank_le_domain
+-/
 
+/- warning: linear_map.rank_zero -> LinearMap.rank_zero is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align linear_map.rank_zero LinearMap.rank_zeroₓ'. -/
 @[simp]
 theorem rank_zero [Nontrivial K] : rank (0 : V →ₗ[K] V') = 0 := by
   rw [rank, LinearMap.range_zero, rank_bot]
@@ -1394,18 +1852,22 @@ theorem rank_zero [Nontrivial K] : rank (0 : V →ₗ[K] V') = 0 := by
 
 variable [AddCommGroup V''] [Module K V'']
 
+#print LinearMap.rank_comp_le_left /-
 theorem rank_comp_le_left (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') : rank (f.comp g) ≤ rank f :=
   by
   refine' rank_le_of_submodule _ _ _
   rw [LinearMap.range_comp]
   exact LinearMap.map_le_range
 #align linear_map.rank_comp_le_left LinearMap.rank_comp_le_left
+-/
 
 variable [AddCommGroup V'₁] [Module K V'₁]
 
+#print LinearMap.rank_comp_le_right /-
 theorem rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) : rank (f.comp g) ≤ rank g := by
   rw [rank, rank, LinearMap.range_comp] <;> exact rank_map_le _ _
 #align linear_map.rank_comp_le_right LinearMap.rank_comp_le_right
+-/
 
 end Ring
 
@@ -1415,6 +1877,12 @@ variable [DivisionRing K] [AddCommGroup V] [Module K V] [AddCommGroup V₁] [Mod
 
 variable [AddCommGroup V'] [Module K V']
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.rank_add_le LinearMap.rank_add_leₓ'. -/
 theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
   calc
     rank (f + g) ≤ Module.rank K (f.range ⊔ g.range : Submodule K V') :=
@@ -1429,12 +1897,24 @@ theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
     
 #align linear_map.rank_add_le LinearMap.rank_add_le
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.rank_finset_sum_le LinearMap.rank_finset_sum_leₓ'. -/
 theorem rank_finset_sum_le {η} (s : Finset η) (f : η → V →ₗ[K] V') :
     rank (∑ d in s, f d) ≤ ∑ d in s, rank (f d) :=
   @Finset.sum_hom_rel _ _ _ _ _ (fun a b => rank a ≤ b) f (fun d => rank (f d)) s
     (le_of_eq rank_zero) fun i g c h => le_trans (rank_add_le _ _) (add_le_add_left h _)
 #align linear_map.rank_finset_sum_le LinearMap.rank_finset_sum_le
 
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 theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'} :
     c ≤ rank f ↔
       ∃ s : Set V,
@@ -1459,6 +1939,12 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'}
     exact inj_on_iff_injective.2 this.injective
 #align linear_map.le_rank_iff_exists_linear_independent LinearMap.le_rank_iff_exists_linearIndependent
 
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+but is expected to have type
+  forall {K : Type.{u1}} {V : Type.{u2}} {V' : Type.{u3}} [_inst_1 : DivisionRing.{u1} K] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_6 : AddCommGroup.{u3} V'] [_inst_7 : Module.{u1, u3} K V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6)] {n : Nat} {f : LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7}, Iff (LE.le.{succ u3} Cardinal.{u3} Cardinal.instLECardinal.{u3} (Nat.cast.{succ u3} Cardinal.{u3} Cardinal.instNatCastCardinal.{u3} n) (LinearMap.rank.{u1, u2, u3} K V V' (DivisionRing.toRing.{u1} K _inst_1) _inst_2 _inst_3 _inst_6 _inst_7 f)) (Exists.{succ u2} (Finset.{u2} V) (fun (s : Finset.{u2} V) => And (Eq.{1} Nat (Finset.card.{u2} V s) n) (LinearIndependent.{u2, u1, u3} (Set.Elem.{u2} V (Finset.toSet.{u2} V s)) K V' (fun (x : Set.Elem.{u2} V (Finset.toSet.{u2} V s)) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearMap.{u1, u1, u2, u3} K K (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1)))) V V' (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : V) => V') _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u3} K K V V' (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_3 _inst_7 (RingHom.id.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K _inst_1))))) f (Subtype.val.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Set.{u2} V) (Set.instMembershipSet.{u2} V) x (Finset.toSet.{u2} V s)) x)) (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V' _inst_6) _inst_7)))
+Case conversion may be inaccurate. Consider using '#align linear_map.le_rank_iff_exists_linear_independent_finset LinearMap.le_rank_iff_exists_linearIndependent_finsetₓ'. -/
 theorem le_rank_iff_exists_linearIndependent_finset {n : ℕ} {f : V →ₗ[K] V'} :
     ↑n ≤ rank f ↔ ∃ s : Finset V, s.card = n ∧ LinearIndependent K fun x : (s : Set V) => f x :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/e05ead7993520a432bec94ac504842d90707ad63

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 
 ! This file was ported from Lean 3 source module linear_algebra.dimension
-! leanprover-community/mathlib commit 3a2039ad20626aebbece10cddb18ef010f7d912d
+! leanprover-community/mathlib commit 45ce3929e3bf9a086a216feea3b1ab6c14bf0e67
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1379,10 +1379,14 @@ def rank (f : V →ₗ[K] V') : Cardinal :=
   Module.rank K f.range
 #align linear_map.rank LinearMap.rank
 
-theorem rank_le_range (f : V →ₗ[K] V₁) : rank f ≤ Module.rank K V₁ :=
+theorem rank_le_range (f : V →ₗ[K] V') : rank f ≤ Module.rank K V' :=
   rank_submodule_le _
 #align linear_map.rank_le_range LinearMap.rank_le_range
 
+theorem rank_le_domain (f : V →ₗ[K] V₁) : rank f ≤ Module.rank K V :=
+  rank_range_le _
+#align linear_map.rank_le_domain LinearMap.rank_le_domain
+
 @[simp]
 theorem rank_zero [Nontrivial K] : rank (0 : V →ₗ[K] V') = 0 := by
   rw [rank, LinearMap.range_zero, rank_bot]
@@ -1390,18 +1394,18 @@ theorem rank_zero [Nontrivial K] : rank (0 : V →ₗ[K] V') = 0 := by
 
 variable [AddCommGroup V''] [Module K V'']
 
-theorem rank_comp_le1 (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') : rank (f.comp g) ≤ rank f :=
+theorem rank_comp_le_left (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') : rank (f.comp g) ≤ rank f :=
   by
   refine' rank_le_of_submodule _ _ _
   rw [LinearMap.range_comp]
   exact LinearMap.map_le_range
-#align linear_map.rank_comp_le1 LinearMap.rank_comp_le1
+#align linear_map.rank_comp_le_left LinearMap.rank_comp_le_left
 
 variable [AddCommGroup V'₁] [Module K V'₁]
 
-theorem rank_comp_le2 (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) : rank (f.comp g) ≤ rank g := by
+theorem rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) : rank (f.comp g) ≤ rank g := by
   rw [rank, rank, LinearMap.range_comp] <;> exact rank_map_le _ _
-#align linear_map.rank_comp_le2 LinearMap.rank_comp_le2
+#align linear_map.rank_comp_le_right LinearMap.rank_comp_le_right
 
 end Ring
 
@@ -1411,12 +1415,6 @@ variable [DivisionRing K] [AddCommGroup V] [Module K V] [AddCommGroup V₁] [Mod
 
 variable [AddCommGroup V'] [Module K V']
 
-theorem rank_le_domain (f : V →ₗ[K] V₁) : rank f ≤ Module.rank K V :=
-  by
-  rw [← rank_range_add_rank_ker f]
-  exact self_le_add_right _ _
-#align linear_map.rank_le_domain LinearMap.rank_le_domain
-
 theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
   calc
     rank (f + g) ≤ Module.rank K (f.range ⊔ g.range : Submodule K V') :=

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 
 ! This file was ported from Lean 3 source module linear_algebra.dimension
-! leanprover-community/mathlib commit e08a42b2dd544cf11eba72e5fc7bf199d4349925
+! leanprover-community/mathlib commit 3a2039ad20626aebbece10cddb18ef010f7d912d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -69,10 +69,6 @@ For vector spaces (i.e. modules over a field), we have
 
 ## Implementation notes
 
-There is a naming discrepancy: most of the theorem names refer to `rank`,
-even though the definition is of `module.rank`.
-This reflects that `module.rank` was originally called `rank`, and only defined for vector spaces.
-
 Many theorems in this file are not universe-generic when they relate dimensions
 in different universes. They should be as general as they can be without
 inserting `lift`s. The types `V`, `V'`, ... all live in different universes,

mathlib commit https://github.com/leanprover-community/mathlib/commit/5ec62c8106221a3f9160e4e4fcc3eed79fe213e9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 
 ! This file was ported from Lean 3 source module linear_algebra.dimension
-! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
+! leanprover-community/mathlib commit e08a42b2dd544cf11eba72e5fc7bf199d4349925
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -882,10 +882,8 @@ theorem Basis.mk_eq_rank'.{m} (v : Basis ι R M) :
 /-- If a module has a finite dimension, all bases are indexed by a finite type. -/
 theorem Basis.nonempty_fintype_index_of_rank_lt_aleph0 {ι : Type _} (b : Basis ι R M)
     (h : Module.rank R M < ℵ₀) : Nonempty (Fintype ι) := by
-  rwa [← Cardinal.lift_lt, ←
-    b.mk_eq_rank,-- ensure `aleph_0` has the correct universe
-    Cardinal.lift_aleph0,
-    ← Cardinal.lift_aleph0.{u_1, v}, Cardinal.lift_lt, Cardinal.lt_aleph0_iff_fintype] at h
+  rwa [← Cardinal.lift_lt, ← b.mk_eq_rank, Cardinal.lift_aleph0, Cardinal.lift_lt_aleph0,
+    Cardinal.lt_aleph0_iff_fintype] at h
 #align basis.nonempty_fintype_index_of_rank_lt_aleph_0 Basis.nonempty_fintype_index_of_rank_lt_aleph0
 
 /-- If a module has a finite dimension, all bases are indexed by a finite type. -/
@@ -972,6 +970,21 @@ variable [AddCommGroup V₁] [Module K V₁] [Module.Free K V₁]
 
 variable {K V}
 
+namespace Module.Free
+
+variable (K V)
+
+/-- The rank of a free module `M` over `R` is the cardinality of `choose_basis_index R M`. -/
+theorem rank_eq_card_chooseBasisIndex : Module.rank K V = (#ChooseBasisIndex K V) :=
+  (chooseBasis K V).mk_eq_rank''.symm
+#align module.free.rank_eq_card_choose_basis_index Module.Free.rank_eq_card_chooseBasisIndex
+
+end Module.Free
+
+open Module.Free
+
+open Cardinal
+
 /-- Two vector spaces are isomorphic if they have the same dimension. -/
 theorem nonempty_linearEquiv_of_lift_rank_eq
     (cond : Cardinal.lift.{v'} (Module.rank K V) = Cardinal.lift.{v} (Module.rank K V')) :
@@ -1021,33 +1034,35 @@ theorem LinearEquiv.nonempty_equiv_iff_rank_eq :
   ⟨fun ⟨h⟩ => LinearEquiv.rank_eq h, fun h => nonempty_linearEquiv_of_rank_eq h⟩
 #align linear_equiv.nonempty_equiv_iff_rank_eq LinearEquiv.nonempty_equiv_iff_rank_eq
 
-theorem rank_prod : Module.rank K (V × V₁) = Module.rank K V + Module.rank K V₁ :=
+/-- The rank of `M × N` is `(module.rank R M).lift + (module.rank R N).lift`. -/
+@[simp]
+theorem rank_prod :
+    Module.rank K (V × V') =
+      Cardinal.lift.{v'} (Module.rank K V) + Cardinal.lift.{v, v'} (Module.rank K V') :=
   by
-  obtain ⟨⟨_, b⟩⟩ := Module.Free.exists_basis K V
-  obtain ⟨⟨_, c⟩⟩ := Module.Free.exists_basis K V₁
-  rw [← Cardinal.lift_inj, ← (Basis.prod b c).mk_eq_rank, Cardinal.lift_add, ← Cardinal.mk_uLift, ←
-    b.mk_eq_rank, ← c.mk_eq_rank, ← Cardinal.mk_uLift, ← Cardinal.mk_uLift,
-    Cardinal.add_def (ULift _)]
-  exact
-    Cardinal.lift_inj.1
-      (Cardinal.lift_mk_eq.2 ⟨equiv.ulift.trans (Equiv.sumCongr Equiv.ulift Equiv.ulift).symm⟩)
+  simpa [rank_eq_card_choose_basis_index K V, rank_eq_card_choose_basis_index K V', lift_umax,
+    lift_umax'] using ((choose_basis K V).Prod (choose_basis K V')).mk_eq_rank.symm
 #align rank_prod rank_prod
 
+/-- If `M` and `N` lie in the same universe, the rank of `M × N` is
+  `(module.rank R M) + (module.rank R N)`. -/
+theorem rank_prod' : Module.rank K (V × V₁) = Module.rank K V + Module.rank K V₁ := by simp
+#align rank_prod' rank_prod'
+
 section Fintype
 
 variable [∀ i, AddCommGroup (φ i)] [∀ i, Module K (φ i)] [∀ i, Module.Free K (φ i)]
 
 open LinearMap
 
+/-- The rank of a finite product is the sum of the ranks. -/
+@[simp]
 theorem rank_pi [Finite η] : Module.rank K (∀ i, φ i) = Cardinal.sum fun i => Module.rank K (φ i) :=
   by
-  haveI := nontrivial_of_invariantBasisNumber K
   cases nonempty_fintype η
-  let b i := (Module.Free.exists_basis K (φ i)).some.2
-  let this : Basis (Σj, _) K (∀ j, φ j) := Pi.basis b
-  rw [← Cardinal.lift_inj, ← this.mk_eq_rank]
-  simp_rw [Cardinal.mk_sigma, Cardinal.lift_sum, ← (b _).mk_range_eq_rank,
-    Cardinal.mk_range_eq _ (b _).Injective]
+  let B i := choose_basis K (φ i)
+  let b : Basis _ K (∀ i, φ i) := Pi.basis fun i => B i
+  simp [← b.mk_eq_rank'', fun i => (B i).mk_eq_rank'']
 #align rank_pi rank_pi
 
 variable [Fintype η]
@@ -1072,13 +1087,6 @@ theorem rank_fin_fun (n : ℕ) : Module.rank K (Fin n → K) = n := by simp [ran
 
 end Fintype
 
-theorem Finsupp.rank_eq {ι : Type v} : Module.rank K (ι →₀ V) = (#ι) * Module.rank K V :=
-  by
-  obtain ⟨⟨_, bs⟩⟩ := Module.Free.exists_basis K V
-  rw [← bs.mk_eq_rank'', ← (Finsupp.basis fun a : ι => bs).mk_eq_rank'', Cardinal.mk_sigma,
-    Cardinal.sum_const']
-#align finsupp.rank_eq Finsupp.rank_eq
-
 -- TODO: merge with the `finrank` content
 /-- An `n`-dimensional `K`-vector space is equivalent to `fin n → K`. -/
 def finDimVectorspaceEquiv (n : ℕ) (hn : Module.rank K V = n) : V ≃ₗ[K] Fin n → K :=
@@ -1134,7 +1142,7 @@ theorem rank_quotient_add_rank (p : Submodule K V) :
     Module.rank K (V ⧸ p) + Module.rank K p = Module.rank K V := by
   classical exact
       let ⟨f⟩ := quotient_prod_linearEquiv p
-      rank_prod.symm.trans f.rank_eq
+      rank_prod'.symm.trans f.rank_eq
 #align rank_quotient_add_rank rank_quotient_add_rank
 
 /-- rank-nullity theorem -/
@@ -1158,7 +1166,7 @@ variable [AddCommGroup V₃] [Module K V₃]
 
 open LinearMap
 
-/-- This is mostly an auxiliary lemma for `rank_sup_add_rank_inf_eq`. -/
+/-- This is mostly an auxiliary lemma for `submodule.rank_sup_add_rank_inf_eq`. -/
 theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd : V₁ →ₗ[K] V₂)
     (ce : V₁ →ₗ[K] V₃) (hde : ⊤ ≤ db.range ⊔ eb.range) (hgd : ker cd = ⊥)
     (eq : db.comp cd = eb.comp ce) (eq₂ : ∀ d e, db d = eb e → ∃ c, cd c = d ∧ ce c = e) :
@@ -1167,7 +1175,7 @@ theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd
   have hf : Surjective (coprod db eb) := by rwa [← range_eq_top, range_coprod, eq_top_iff]
   conv =>
     rhs
-    rw [← rank_prod, rank_eq_of_surjective _ hf]
+    rw [← rank_prod', rank_eq_of_surjective _ hf]
   congr 1
   apply LinearEquiv.rank_eq
   refine' LinearEquiv.ofBijective _ ⟨_, _⟩
@@ -1189,7 +1197,7 @@ theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd
     rw [h₂, _root_.neg_neg]
 #align rank_add_rank_split rank_add_rank_split
 
-theorem rank_sup_add_rank_inf_eq (s t : Submodule K V) :
+theorem Submodule.rank_sup_add_rank_inf_eq (s t : Submodule K V) :
     Module.rank K (s ⊔ t : Submodule K V) + Module.rank K (s ⊓ t : Submodule K V) =
       Module.rank K s + Module.rank K t :=
   rank_add_rank_split (ofLe le_sup_left) (ofLe le_sup_right) (ofLe inf_le_left) (ofLe inf_le_right)
@@ -1203,14 +1211,14 @@ theorem rank_sup_add_rank_inf_eq (s t : Submodule K V) :
       rintro ⟨b₁, hb₁⟩ ⟨b₂, hb₂⟩ eq
       obtain rfl : b₁ = b₂ := congr_arg Subtype.val Eq
       exact ⟨⟨b₁, hb₁, hb₂⟩, rfl, rfl⟩)
-#align rank_sup_add_rank_inf_eq rank_sup_add_rank_inf_eq
+#align submodule.rank_sup_add_rank_inf_eq Submodule.rank_sup_add_rank_inf_eq
 
-theorem rank_add_le_rank_add_rank (s t : Submodule K V) :
+theorem Submodule.rank_add_le_rank_add_rank (s t : Submodule K V) :
     Module.rank K (s ⊔ t : Submodule K V) ≤ Module.rank K s + Module.rank K t :=
   by
-  rw [← rank_sup_add_rank_inf_eq]
+  rw [← Submodule.rank_sup_add_rank_inf_eq]
   exact self_le_add_right _ _
-#align rank_add_le_rank_add_rank rank_add_le_rank_add_rank
+#align submodule.rank_add_le_rank_add_rank Submodule.rank_add_le_rank_add_rank
 
 end
 
@@ -1423,7 +1431,7 @@ theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
           eq_top_iff'.2 fun x =>
             show f x + g x ∈ (f.range ⊔ g.range : Submodule K V') from
               mem_sup.2 ⟨_, ⟨x, rfl⟩, _, ⟨x, rfl⟩, rfl⟩
-    _ ≤ rank f + rank g := rank_add_le_rank_add_rank _ _
+    _ ≤ rank f + rank g := Submodule.rank_add_le_rank_add_rank _ _
     
 #align linear_map.rank_add_le LinearMap.rank_add_le
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 
 ! This file was ported from Lean 3 source module linear_algebra.dimension
-! leanprover-community/mathlib commit be2ac64be57e8319fcd5c5547f3a8d9412daf5ec
+! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -28,9 +28,9 @@ import Mathbin.SetTheory.Cardinal.Cofinality
 
 ## Main statements
 
-* `linear_map.dim_le_of_injective`: the source of an injective linear map has dimension
+* `linear_map.rank_le_of_injective`: the source of an injective linear map has dimension
   at most that of the target.
-* `linear_map.dim_le_of_surjective`: the target of a surjective linear map has dimension
+* `linear_map.rank_le_of_surjective`: the target of a surjective linear map has dimension
   at most that of that source.
 * `basis_fintype_of_finite_spans`:
   the existence of a finite spanning set implies that any basis is finite.
@@ -63,15 +63,15 @@ For modules over rings with invariant basis number
 
 For vector spaces (i.e. modules over a field), we have
 
-* `dim_quotient_add_dim`: if `V₁` is a submodule of `V`, then
+* `rank_quotient_add_rank`: if `V₁` is a submodule of `V`, then
   `module.rank (V/V₁) + module.rank V₁ = module.rank V`.
-* `dim_range_add_dim_ker`: the rank-nullity theorem.
+* `rank_range_add_rank_ker`: the rank-nullity theorem.
 
 ## Implementation notes
 
-There is a naming discrepancy: most of the theorem names refer to `dim`,
+There is a naming discrepancy: most of the theorem names refer to `rank`,
 even though the definition is of `module.rank`.
-This reflects that `module.rank` was originally called `dim`, and only defined for vector spaces.
+This reflects that `module.rank` was originally called `rank`, and only defined for vector spaces.
 
 Many theorems in this file are not universe-generic when they relate dimensions
 in different universes. They should be as general as they can be without
@@ -131,7 +131,7 @@ variable {M' : Type v'} [AddCommGroup M'] [Module R M']
 
 variable {M₁ : Type v} [AddCommGroup M₁] [Module R M₁]
 
-theorem LinearMap.lift_dim_le_of_injective (f : M →ₗ[R] M') (i : Injective f) :
+theorem LinearMap.lift_rank_le_of_injective (f : M →ₗ[R] M') (i : Injective f) :
     Cardinal.lift.{v'} (Module.rank R M) ≤ Cardinal.lift.{v} (Module.rank R M') :=
   by
   dsimp [Module.rank]
@@ -141,23 +141,23 @@ theorem LinearMap.lift_dim_le_of_injective (f : M →ₗ[R] M') (i : Injective f
   rintro ⟨s, li⟩
   refine' ⟨⟨f '' s, _⟩, cardinal.lift_mk_le'.mpr ⟨(Equiv.Set.image f s i).toEmbedding⟩⟩
   exact (li.map' _ <| linear_map.ker_eq_bot.mpr i).image
-#align linear_map.lift_dim_le_of_injective LinearMap.lift_dim_le_of_injective
+#align linear_map.lift_rank_le_of_injective LinearMap.lift_rank_le_of_injective
 
-theorem LinearMap.dim_le_of_injective (f : M →ₗ[R] M₁) (i : Injective f) :
+theorem LinearMap.rank_le_of_injective (f : M →ₗ[R] M₁) (i : Injective f) :
     Module.rank R M ≤ Module.rank R M₁ :=
-  Cardinal.lift_le.1 (f.lift_dim_le_of_injective i)
-#align linear_map.dim_le_of_injective LinearMap.dim_le_of_injective
+  Cardinal.lift_le.1 (f.lift_rank_le_of_injective i)
+#align linear_map.rank_le_of_injective LinearMap.rank_le_of_injective
 
-theorem dim_le {n : ℕ}
+theorem rank_le {n : ℕ}
     (H : ∀ s : Finset M, (LinearIndependent R fun i : s => (i : M)) → s.card ≤ n) :
     Module.rank R M ≤ n := by
   rw [Module.rank]
   apply csupᵢ_le'
   rintro ⟨s, li⟩
   exact linearIndependent_bounded_of_finset_linearIndependent_bounded H _ li
-#align dim_le dim_le
+#align rank_le rank_le
 
-theorem lift_dim_range_le (f : M →ₗ[R] M') :
+theorem lift_rank_range_le (f : M →ₗ[R] M') :
     Cardinal.lift.{v} (Module.rank R f.range) ≤ Cardinal.lift.{v'} (Module.rank R M) :=
   by
   dsimp [Module.rank]
@@ -171,89 +171,90 @@ theorem lift_dim_range_le (f : M →ₗ[R] M') :
   · apply LinearIndependent.of_comp f.range_restrict
     convert li.comp (Equiv.Set.rangeSplittingImageEquiv f s) (Equiv.injective _) using 1
   · exact (cardinal.lift_mk_eq'.mpr ⟨Equiv.Set.rangeSplittingImageEquiv f s⟩).ge
-#align lift_dim_range_le lift_dim_range_le
+#align lift_rank_range_le lift_rank_range_le
 
-theorem dim_range_le (f : M →ₗ[R] M₁) : Module.rank R f.range ≤ Module.rank R M := by
-  simpa using lift_dim_range_le f
-#align dim_range_le dim_range_le
+theorem rank_range_le (f : M →ₗ[R] M₁) : Module.rank R f.range ≤ Module.rank R M := by
+  simpa using lift_rank_range_le f
+#align rank_range_le rank_range_le
 
-theorem lift_dim_map_le (f : M →ₗ[R] M') (p : Submodule R M) :
+theorem lift_rank_map_le (f : M →ₗ[R] M') (p : Submodule R M) :
     Cardinal.lift.{v} (Module.rank R (p.map f)) ≤ Cardinal.lift.{v'} (Module.rank R p) :=
   by
-  have h := lift_dim_range_le (f.comp (Submodule.subtype p))
+  have h := lift_rank_range_le (f.comp (Submodule.subtype p))
   rwa [LinearMap.range_comp, range_subtype] at h
-#align lift_dim_map_le lift_dim_map_le
+#align lift_rank_map_le lift_rank_map_le
 
-theorem dim_map_le (f : M →ₗ[R] M₁) (p : Submodule R M) :
-    Module.rank R (p.map f) ≤ Module.rank R p := by simpa using lift_dim_map_le f p
-#align dim_map_le dim_map_le
+theorem rank_map_le (f : M →ₗ[R] M₁) (p : Submodule R M) :
+    Module.rank R (p.map f) ≤ Module.rank R p := by simpa using lift_rank_map_le f p
+#align rank_map_le rank_map_le
 
-theorem dim_le_of_submodule (s t : Submodule R M) (h : s ≤ t) : Module.rank R s ≤ Module.rank R t :=
-  (ofLe h).dim_le_of_injective fun ⟨x, hx⟩ ⟨y, hy⟩ eq =>
+theorem rank_le_of_submodule (s t : Submodule R M) (h : s ≤ t) :
+    Module.rank R s ≤ Module.rank R t :=
+  (ofLe h).rank_le_of_injective fun ⟨x, hx⟩ ⟨y, hy⟩ eq =>
     Subtype.eq <| show x = y from Subtype.ext_iff_val.1 Eq
-#align dim_le_of_submodule dim_le_of_submodule
+#align rank_le_of_submodule rank_le_of_submodule
 
 /-- Two linearly equivalent vector spaces have the same dimension, a version with different
 universes. -/
-theorem LinearEquiv.lift_dim_eq (f : M ≃ₗ[R] M') :
+theorem LinearEquiv.lift_rank_eq (f : M ≃ₗ[R] M') :
     Cardinal.lift.{v'} (Module.rank R M) = Cardinal.lift.{v} (Module.rank R M') :=
   by
   apply le_antisymm
-  · exact f.to_linear_map.lift_dim_le_of_injective f.injective
-  · exact f.symm.to_linear_map.lift_dim_le_of_injective f.symm.injective
-#align linear_equiv.lift_dim_eq LinearEquiv.lift_dim_eq
+  · exact f.to_linear_map.lift_rank_le_of_injective f.injective
+  · exact f.symm.to_linear_map.lift_rank_le_of_injective f.symm.injective
+#align linear_equiv.lift_rank_eq LinearEquiv.lift_rank_eq
 
 /-- Two linearly equivalent vector spaces have the same dimension. -/
-theorem LinearEquiv.dim_eq (f : M ≃ₗ[R] M₁) : Module.rank R M = Module.rank R M₁ :=
-  Cardinal.lift_inj.1 f.lift_dim_eq
-#align linear_equiv.dim_eq LinearEquiv.dim_eq
+theorem LinearEquiv.rank_eq (f : M ≃ₗ[R] M₁) : Module.rank R M = Module.rank R M₁ :=
+  Cardinal.lift_inj.1 f.lift_rank_eq
+#align linear_equiv.rank_eq LinearEquiv.rank_eq
 
-theorem dim_eq_of_injective (f : M →ₗ[R] M₁) (h : Injective f) :
+theorem rank_eq_of_injective (f : M →ₗ[R] M₁) (h : Injective f) :
     Module.rank R M = Module.rank R f.range :=
-  (LinearEquiv.ofInjective f h).dim_eq
-#align dim_eq_of_injective dim_eq_of_injective
+  (LinearEquiv.ofInjective f h).rank_eq
+#align rank_eq_of_injective rank_eq_of_injective
 
 /-- Pushforwards of submodules along a `linear_equiv` have the same dimension. -/
-theorem LinearEquiv.dim_map_eq (f : M ≃ₗ[R] M₁) (p : Submodule R M) :
+theorem LinearEquiv.rank_map_eq (f : M ≃ₗ[R] M₁) (p : Submodule R M) :
     Module.rank R (p.map (f : M →ₗ[R] M₁)) = Module.rank R p :=
-  (f.submoduleMap p).dim_eq.symm
-#align linear_equiv.dim_map_eq LinearEquiv.dim_map_eq
+  (f.submoduleMap p).rank_eq.symm
+#align linear_equiv.rank_map_eq LinearEquiv.rank_map_eq
 
 variable (R M)
 
 @[simp]
-theorem dim_top : Module.rank R (⊤ : Submodule R M) = Module.rank R M :=
+theorem rank_top : Module.rank R (⊤ : Submodule R M) = Module.rank R M :=
   by
   have : (⊤ : Submodule R M) ≃ₗ[R] M := LinearEquiv.ofTop ⊤ rfl
-  rw [this.dim_eq]
-#align dim_top dim_top
+  rw [this.rank_eq]
+#align rank_top rank_top
 
 variable {R M}
 
-theorem dim_range_of_surjective (f : M →ₗ[R] M') (h : Surjective f) :
-    Module.rank R f.range = Module.rank R M' := by rw [LinearMap.range_eq_top.2 h, dim_top]
-#align dim_range_of_surjective dim_range_of_surjective
+theorem rank_range_of_surjective (f : M →ₗ[R] M') (h : Surjective f) :
+    Module.rank R f.range = Module.rank R M' := by rw [LinearMap.range_eq_top.2 h, rank_top]
+#align rank_range_of_surjective rank_range_of_surjective
 
-theorem dim_submodule_le (s : Submodule R M) : Module.rank R s ≤ Module.rank R M :=
+theorem rank_submodule_le (s : Submodule R M) : Module.rank R s ≤ Module.rank R M :=
   by
-  rw [← dim_top R M]
-  exact dim_le_of_submodule _ _ le_top
-#align dim_submodule_le dim_submodule_le
+  rw [← rank_top R M]
+  exact rank_le_of_submodule _ _ le_top
+#align rank_submodule_le rank_submodule_le
 
-theorem LinearMap.dim_le_of_surjective (f : M →ₗ[R] M₁) (h : Surjective f) :
+theorem LinearMap.rank_le_of_surjective (f : M →ₗ[R] M₁) (h : Surjective f) :
     Module.rank R M₁ ≤ Module.rank R M :=
   by
-  rw [← dim_range_of_surjective f h]
-  apply dim_range_le
-#align linear_map.dim_le_of_surjective LinearMap.dim_le_of_surjective
+  rw [← rank_range_of_surjective f h]
+  apply rank_range_le
+#align linear_map.rank_le_of_surjective LinearMap.rank_le_of_surjective
 
-theorem dim_quotient_le (p : Submodule R M) : Module.rank R (M ⧸ p) ≤ Module.rank R M :=
-  (mkQ p).dim_le_of_surjective (surjective_quot_mk _)
-#align dim_quotient_le dim_quotient_le
+theorem rank_quotient_le (p : Submodule R M) : Module.rank R (M ⧸ p) ≤ Module.rank R M :=
+  (mkQ p).rank_le_of_surjective (surjective_quot_mk _)
+#align rank_quotient_le rank_quotient_le
 
 variable [Nontrivial R]
 
-theorem cardinal_lift_le_dim_of_linearIndependent.{m} {ι : Type w} {v : ι → M}
+theorem cardinal_lift_le_rank_of_linearIndependent.{m} {ι : Type w} {v : ι → M}
     (hv : LinearIndependent R v) :
     Cardinal.lift.{max v m} (#ι) ≤ Cardinal.lift.{max w m} (Module.rank R M) :=
   by
@@ -264,26 +265,27 @@ theorem cardinal_lift_le_dim_of_linearIndependent.{m} {ι : Type w} {v : ι →
     swap
     exact le_csupᵢ (Cardinal.bddAbove_range.{v, v} _) ⟨range v, hv.coe_range⟩
     exact le_rfl
-#align cardinal_lift_le_dim_of_linear_independent cardinal_lift_le_dim_of_linearIndependent
+#align cardinal_lift_le_rank_of_linear_independent cardinal_lift_le_rank_of_linearIndependent
 
-theorem cardinal_lift_le_dim_of_linear_independent' {ι : Type w} {v : ι → M}
+theorem cardinal_lift_le_rank_of_linear_independent' {ι : Type w} {v : ι → M}
     (hv : LinearIndependent R v) : Cardinal.lift.{v} (#ι) ≤ Cardinal.lift.{w} (Module.rank R M) :=
-  cardinal_lift_le_dim_of_linearIndependent.{u, v, w, 0} hv
-#align cardinal_lift_le_dim_of_linear_independent' cardinal_lift_le_dim_of_linear_independent'
+  cardinal_lift_le_rank_of_linearIndependent.{u, v, w, 0} hv
+#align cardinal_lift_le_rank_of_linear_independent' cardinal_lift_le_rank_of_linear_independent'
 
-theorem cardinal_le_dim_of_linearIndependent {ι : Type v} {v : ι → M} (hv : LinearIndependent R v) :
-    (#ι) ≤ Module.rank R M := by simpa using cardinal_lift_le_dim_of_linearIndependent hv
-#align cardinal_le_dim_of_linear_independent cardinal_le_dim_of_linearIndependent
+theorem cardinal_le_rank_of_linearIndependent {ι : Type v} {v : ι → M}
+    (hv : LinearIndependent R v) : (#ι) ≤ Module.rank R M := by
+  simpa using cardinal_lift_le_rank_of_linearIndependent hv
+#align cardinal_le_rank_of_linear_independent cardinal_le_rank_of_linearIndependent
 
-theorem cardinal_le_dim_of_linear_independent' {s : Set M}
+theorem cardinal_le_rank_of_linear_independent' {s : Set M}
     (hs : LinearIndependent R (fun x => x : s → M)) : (#s) ≤ Module.rank R M :=
-  cardinal_le_dim_of_linearIndependent hs
-#align cardinal_le_dim_of_linear_independent' cardinal_le_dim_of_linear_independent'
+  cardinal_le_rank_of_linearIndependent hs
+#align cardinal_le_rank_of_linear_independent' cardinal_le_rank_of_linear_independent'
 
 variable (R M)
 
 @[simp]
-theorem dim_pUnit : Module.rank R PUnit = 0 :=
+theorem rank_pUnit : Module.rank R PUnit = 0 :=
   by
   apply le_bot_iff.mp
   rw [Module.rank]
@@ -295,21 +297,21 @@ theorem dim_pUnit : Module.rank R PUnit = 0 :=
   by_contra h
   obtain ⟨a, ha⟩ := nonempty_iff_ne_empty.2 h
   simpa using LinearIndependent.ne_zero (⟨a, ha⟩ : s) li
-#align dim_punit dim_pUnit
+#align rank_punit rank_pUnit
 
 @[simp]
-theorem dim_bot : Module.rank R (⊥ : Submodule R M) = 0 :=
+theorem rank_bot : Module.rank R (⊥ : Submodule R M) = 0 :=
   by
   have : (⊥ : Submodule R M) ≃ₗ[R] PUnit := bot_equiv_punit
-  rw [this.dim_eq, dim_pUnit]
-#align dim_bot dim_bot
+  rw [this.rank_eq, rank_pUnit]
+#align rank_bot rank_bot
 
 variable {R M}
 
-theorem exists_mem_ne_zero_of_dim_pos {s : Submodule R M} (h : 0 < Module.rank R s) :
+theorem exists_mem_ne_zero_of_rank_pos {s : Submodule R M} (h : 0 < Module.rank R s) :
     ∃ b : M, b ∈ s ∧ b ≠ 0 :=
-  exists_mem_ne_zero_of_ne_bot fun eq => by rw [Eq, dim_bot] at h <;> exact lt_irrefl _ h
-#align exists_mem_ne_zero_of_dim_pos exists_mem_ne_zero_of_dim_pos
+  exists_mem_ne_zero_of_ne_bot fun eq => by rw [Eq, rank_bot] at h <;> exact lt_irrefl _ h
+#align exists_mem_ne_zero_of_rank_pos exists_mem_ne_zero_of_rank_pos
 
 /-- A linearly-independent family of vectors in a module over a non-trivial ring must be finite if
 the module is Noetherian. -/
@@ -481,7 +483,7 @@ theorem CompleteLattice.Independent.subtype_ne_bot_le_rank [NoZeroSMulDivisors R
     exact i.prop
   choose v hvV hv using hI
   have : LinearIndependent R v := (hV.comp Subtype.coe_injective).LinearIndependent _ hvV hv
-  exact cardinal_lift_le_dim_of_linear_independent' this
+  exact cardinal_lift_le_rank_of_linear_independent' this
 #align complete_lattice.independent.subtype_ne_bot_le_rank CompleteLattice.Independent.subtype_ne_bot_le_rank
 
 end
@@ -493,7 +495,7 @@ variable {R : Type u} {M : Type v}
 variable [Ring R] [AddCommGroup M] [Module R M]
 
 @[simp]
-theorem dim_subsingleton [Subsingleton R] : Module.rank R M = 1 :=
+theorem rank_subsingleton [Subsingleton R] : Module.rank R M = 1 :=
   by
   haveI := Module.subsingleton R M
   have : Nonempty { s : Set M // LinearIndependent R (coe : s → M) } :=
@@ -508,49 +510,49 @@ theorem dim_subsingleton [Subsingleton R] : Module.rank R M = 1 :=
     intros
     exact Subsingleton.elim _ _
   · exact hw.trans_eq (Cardinal.mk_singleton _).symm
-#align dim_subsingleton dim_subsingleton
+#align rank_subsingleton rank_subsingleton
 
 variable [NoZeroSMulDivisors R M]
 
-theorem dim_pos [Nontrivial M] : 0 < Module.rank R M :=
+theorem rank_pos [Nontrivial M] : 0 < Module.rank R M :=
   by
   obtain ⟨x, hx⟩ := exists_ne (0 : M)
   suffices 1 ≤ Module.rank R M by exact zero_lt_one.trans_le this
   letI := Module.nontrivial R M
   suffices LinearIndependent R fun y : ({x} : Set M) => ↑y by
-    simpa using cardinal_le_dim_of_linearIndependent this
+    simpa using cardinal_le_rank_of_linearIndependent this
   exact linearIndependent_singleton hx
-#align dim_pos dim_pos
+#align rank_pos rank_pos
 
 variable [Nontrivial R]
 
-theorem dim_zero_iff_forall_zero : Module.rank R M = 0 ↔ ∀ x : M, x = 0 :=
+theorem rank_zero_iff_forall_zero : Module.rank R M = 0 ↔ ∀ x : M, x = 0 :=
   by
   refine' ⟨fun h => _, fun h => _⟩
   · contrapose! h
     obtain ⟨x, hx⟩ := h
     letI : Nontrivial M := nontrivial_of_ne _ _ hx
-    exact dim_pos.ne'
+    exact rank_pos.ne'
   · have : (⊤ : Submodule R M) = ⊥ := by
       ext x
       simp [h x]
-    rw [← dim_top, this, dim_bot]
-#align dim_zero_iff_forall_zero dim_zero_iff_forall_zero
+    rw [← rank_top, this, rank_bot]
+#align rank_zero_iff_forall_zero rank_zero_iff_forall_zero
 
-/-- See `dim_subsingleton` for the reason that `nontrivial R` is needed. -/
-theorem dim_zero_iff : Module.rank R M = 0 ↔ Subsingleton M :=
-  dim_zero_iff_forall_zero.trans (subsingleton_iff_forall_eq 0).symm
-#align dim_zero_iff dim_zero_iff
+/-- See `rank_subsingleton` for the reason that `nontrivial R` is needed. -/
+theorem rank_zero_iff : Module.rank R M = 0 ↔ Subsingleton M :=
+  rank_zero_iff_forall_zero.trans (subsingleton_iff_forall_eq 0).symm
+#align rank_zero_iff rank_zero_iff
 
-theorem dim_pos_iff_exists_ne_zero : 0 < Module.rank R M ↔ ∃ x : M, x ≠ 0 :=
+theorem rank_pos_iff_exists_ne_zero : 0 < Module.rank R M ↔ ∃ x : M, x ≠ 0 :=
   by
   rw [← not_iff_not]
-  simpa using dim_zero_iff_forall_zero
-#align dim_pos_iff_exists_ne_zero dim_pos_iff_exists_ne_zero
+  simpa using rank_zero_iff_forall_zero
+#align rank_pos_iff_exists_ne_zero rank_pos_iff_exists_ne_zero
 
-theorem dim_pos_iff_nontrivial : 0 < Module.rank R M ↔ Nontrivial M :=
-  dim_pos_iff_exists_ne_zero.trans (nontrivial_iff_exists_ne 0).symm
-#align dim_pos_iff_nontrivial dim_pos_iff_nontrivial
+theorem rank_pos_iff_nontrivial : 0 < Module.rank R M ↔ Nontrivial M :=
+  rank_pos_iff_exists_ne_zero.trans (nontrivial_iff_exists_ne 0).symm
+#align rank_pos_iff_nontrivial rank_pos_iff_nontrivial
 
 end RankZero
 
@@ -813,7 +815,7 @@ theorem maximal_linearIndependent_eq_infinite_basis {ι : Type _} (b : Basis ι
     exact infinite_basis_le_maximal_linearIndependent b v i m
 #align maximal_linear_independent_eq_infinite_basis maximal_linearIndependent_eq_infinite_basis
 
-theorem Basis.mk_eq_dim'' {ι : Type v} (v : Basis ι R M) : (#ι) = Module.rank R M :=
+theorem Basis.mk_eq_rank'' {ι : Type v} (v : Basis ι R M) : (#ι) = Module.rank R M :=
   by
   haveI := nontrivial_of_invariantBasisNumber R
   rw [Module.rank]
@@ -830,28 +832,28 @@ theorem Basis.mk_eq_dim'' {ι : Type v} (v : Basis ι R M) : (#ι) = Module.rank
   · apply csupᵢ_le'
     rintro ⟨s, li⟩
     apply linearIndependent_le_basis v _ li
-#align basis.mk_eq_dim'' Basis.mk_eq_dim''
+#align basis.mk_eq_rank'' Basis.mk_eq_rank''
 
-theorem Basis.mk_range_eq_dim (v : Basis ι R M) : (#range v) = Module.rank R M :=
-  v.reindexRange.mk_eq_dim''
-#align basis.mk_range_eq_dim Basis.mk_range_eq_dim
+theorem Basis.mk_range_eq_rank (v : Basis ι R M) : (#range v) = Module.rank R M :=
+  v.reindexRange.mk_eq_rank''
+#align basis.mk_range_eq_rank Basis.mk_range_eq_rank
 
 /-- If a vector space has a finite basis, then its dimension (seen as a cardinal) is equal to the
 cardinality of the basis. -/
-theorem dim_eq_card_basis {ι : Type w} [Fintype ι] (h : Basis ι R M) :
+theorem rank_eq_card_basis {ι : Type w} [Fintype ι] (h : Basis ι R M) :
     Module.rank R M = Fintype.card ι :=
   by
   haveI := nontrivial_of_invariantBasisNumber R
-  rw [← h.mk_range_eq_dim, Cardinal.mk_fintype, Set.card_range_of_injective h.injective]
-#align dim_eq_card_basis dim_eq_card_basis
+  rw [← h.mk_range_eq_rank, Cardinal.mk_fintype, Set.card_range_of_injective h.injective]
+#align rank_eq_card_basis rank_eq_card_basis
 
 theorem Basis.card_le_card_of_linearIndependent {ι : Type _} [Fintype ι] (b : Basis ι R M)
     {ι' : Type _} [Fintype ι'] {v : ι' → M} (hv : LinearIndependent R v) :
     Fintype.card ι' ≤ Fintype.card ι :=
   by
   letI := nontrivial_of_invariantBasisNumber R
-  simpa [dim_eq_card_basis b, Cardinal.mk_fintype] using
-    cardinal_lift_le_dim_of_linear_independent' hv
+  simpa [rank_eq_card_basis b, Cardinal.mk_fintype] using
+    cardinal_lift_le_rank_of_linear_independent' hv
 #align basis.card_le_card_of_linear_independent Basis.card_le_card_of_linearIndependent
 
 theorem Basis.card_le_card_of_submodule (N : Submodule R M) [Fintype ι] (b : Basis ι R M)
@@ -865,53 +867,53 @@ theorem Basis.card_le_card_of_le {N O : Submodule R M} (hNO : N ≤ O) [Fintype
     (b'.LinearIndependent.map' (Submodule.ofLe hNO) (N.ker_ofLe O _))
 #align basis.card_le_card_of_le Basis.card_le_card_of_le
 
-theorem Basis.mk_eq_dim (v : Basis ι R M) :
+theorem Basis.mk_eq_rank (v : Basis ι R M) :
     Cardinal.lift.{v} (#ι) = Cardinal.lift.{w} (Module.rank R M) :=
   by
   haveI := nontrivial_of_invariantBasisNumber R
-  rw [← v.mk_range_eq_dim, Cardinal.mk_range_eq_of_injective v.injective]
-#align basis.mk_eq_dim Basis.mk_eq_dim
+  rw [← v.mk_range_eq_rank, Cardinal.mk_range_eq_of_injective v.injective]
+#align basis.mk_eq_rank Basis.mk_eq_rank
 
-theorem Basis.mk_eq_dim'.{m} (v : Basis ι R M) :
+theorem Basis.mk_eq_rank'.{m} (v : Basis ι R M) :
     Cardinal.lift.{max v m} (#ι) = Cardinal.lift.{max w m} (Module.rank R M) := by
-  simpa using v.mk_eq_dim
-#align basis.mk_eq_dim' Basis.mk_eq_dim'
+  simpa using v.mk_eq_rank
+#align basis.mk_eq_rank' Basis.mk_eq_rank'
 
 /-- If a module has a finite dimension, all bases are indexed by a finite type. -/
-theorem Basis.nonempty_fintype_index_of_dim_lt_aleph0 {ι : Type _} (b : Basis ι R M)
+theorem Basis.nonempty_fintype_index_of_rank_lt_aleph0 {ι : Type _} (b : Basis ι R M)
     (h : Module.rank R M < ℵ₀) : Nonempty (Fintype ι) := by
   rwa [← Cardinal.lift_lt, ←
-    b.mk_eq_dim,-- ensure `aleph_0` has the correct universe
+    b.mk_eq_rank,-- ensure `aleph_0` has the correct universe
     Cardinal.lift_aleph0,
     ← Cardinal.lift_aleph0.{u_1, v}, Cardinal.lift_lt, Cardinal.lt_aleph0_iff_fintype] at h
-#align basis.nonempty_fintype_index_of_dim_lt_aleph_0 Basis.nonempty_fintype_index_of_dim_lt_aleph0
+#align basis.nonempty_fintype_index_of_rank_lt_aleph_0 Basis.nonempty_fintype_index_of_rank_lt_aleph0
 
 /-- If a module has a finite dimension, all bases are indexed by a finite type. -/
-noncomputable def Basis.fintypeIndexOfDimLtAleph0 {ι : Type _} (b : Basis ι R M)
+noncomputable def Basis.fintypeIndexOfRankLtAleph0 {ι : Type _} (b : Basis ι R M)
     (h : Module.rank R M < ℵ₀) : Fintype ι :=
-  Classical.choice (b.nonempty_fintype_index_of_dim_lt_aleph0 h)
-#align basis.fintype_index_of_dim_lt_aleph_0 Basis.fintypeIndexOfDimLtAleph0
+  Classical.choice (b.nonempty_fintype_index_of_rank_lt_aleph0 h)
+#align basis.fintype_index_of_rank_lt_aleph_0 Basis.fintypeIndexOfRankLtAleph0
 
 /-- If a module has a finite dimension, all bases are indexed by a finite set. -/
-theorem Basis.finite_index_of_dim_lt_aleph0 {ι : Type _} {s : Set ι} (b : Basis s R M)
+theorem Basis.finite_index_of_rank_lt_aleph0 {ι : Type _} {s : Set ι} (b : Basis s R M)
     (h : Module.rank R M < ℵ₀) : s.Finite :=
-  finite_def.2 (b.nonempty_fintype_index_of_dim_lt_aleph0 h)
-#align basis.finite_index_of_dim_lt_aleph_0 Basis.finite_index_of_dim_lt_aleph0
+  finite_def.2 (b.nonempty_fintype_index_of_rank_lt_aleph0 h)
+#align basis.finite_index_of_rank_lt_aleph_0 Basis.finite_index_of_rank_lt_aleph0
 
-theorem dim_span {v : ι → M} (hv : LinearIndependent R v) :
+theorem rank_span {v : ι → M} (hv : LinearIndependent R v) :
     Module.rank R ↥(span R (range v)) = (#range v) :=
   by
   haveI := nontrivial_of_invariantBasisNumber R
-  rw [← Cardinal.lift_inj, ← (Basis.span hv).mk_eq_dim,
+  rw [← Cardinal.lift_inj, ← (Basis.span hv).mk_eq_rank,
     Cardinal.mk_range_eq_of_injective (@LinearIndependent.injective ι R M v _ _ _ _ hv)]
-#align dim_span dim_span
+#align rank_span rank_span
 
-theorem dim_span_set {s : Set M} (hs : LinearIndependent R (fun x => x : s → M)) :
+theorem rank_span_set {s : Set M} (hs : LinearIndependent R (fun x => x : s → M)) :
     Module.rank R ↥(span R s) = (#s) :=
   by
   rw [← @set_of_mem_eq _ s, ← Subtype.range_coe_subtype]
-  exact dim_span hs
-#align dim_span_set dim_span_set
+  exact rank_span hs
+#align rank_span_set rank_span_set
 
 /-- If `N` is a submodule in a free, finitely generated module,
 do induction on adjoining a linear independent element to a submodule. -/
@@ -952,9 +954,9 @@ theorem Ideal.rank_eq {R S : Type _} [CommRing R] [StrongRankCondition R] [Ring
 variable (R)
 
 @[simp]
-theorem dim_self : Module.rank R R = 1 := by
-  rw [← Cardinal.lift_inj, ← (Basis.singleton PUnit R).mk_eq_dim, Cardinal.mk_pUnit]
-#align dim_self dim_self
+theorem rank_self : Module.rank R R = 1 := by
+  rw [← Cardinal.lift_inj, ← (Basis.singleton PUnit R).mk_eq_rank, Cardinal.mk_pUnit]
+#align rank_self rank_self
 
 end StrongRankCondition
 
@@ -971,65 +973,65 @@ variable [AddCommGroup V₁] [Module K V₁] [Module.Free K V₁]
 variable {K V}
 
 /-- Two vector spaces are isomorphic if they have the same dimension. -/
-theorem nonempty_linearEquiv_of_lift_dim_eq
+theorem nonempty_linearEquiv_of_lift_rank_eq
     (cond : Cardinal.lift.{v'} (Module.rank K V) = Cardinal.lift.{v} (Module.rank K V')) :
     Nonempty (V ≃ₗ[K] V') :=
   by
   obtain ⟨⟨_, B⟩⟩ := Module.Free.exists_basis K V
   obtain ⟨⟨_, B'⟩⟩ := Module.Free.exists_basis K V'
   have : Cardinal.lift.{v', v} (#_) = Cardinal.lift.{v, v'} (#_) := by
-    rw [B.mk_eq_dim'', cond, B'.mk_eq_dim'']
+    rw [B.mk_eq_rank'', cond, B'.mk_eq_rank'']
   exact (Cardinal.lift_mk_eq.{v, v', 0}.1 this).map (B.equiv B')
-#align nonempty_linear_equiv_of_lift_dim_eq nonempty_linearEquiv_of_lift_dim_eq
+#align nonempty_linear_equiv_of_lift_rank_eq nonempty_linearEquiv_of_lift_rank_eq
 
 /-- Two vector spaces are isomorphic if they have the same dimension. -/
-theorem nonempty_linearEquiv_of_dim_eq (cond : Module.rank K V = Module.rank K V₁) :
+theorem nonempty_linearEquiv_of_rank_eq (cond : Module.rank K V = Module.rank K V₁) :
     Nonempty (V ≃ₗ[K] V₁) :=
-  nonempty_linearEquiv_of_lift_dim_eq <| congr_arg _ cond
-#align nonempty_linear_equiv_of_dim_eq nonempty_linearEquiv_of_dim_eq
+  nonempty_linearEquiv_of_lift_rank_eq <| congr_arg _ cond
+#align nonempty_linear_equiv_of_rank_eq nonempty_linearEquiv_of_rank_eq
 
 section
 
 variable (V V' V₁)
 
 /-- Two vector spaces are isomorphic if they have the same dimension. -/
-def LinearEquiv.ofLiftDimEq
+def LinearEquiv.ofLiftRankEq
     (cond : Cardinal.lift.{v'} (Module.rank K V) = Cardinal.lift.{v} (Module.rank K V')) :
     V ≃ₗ[K] V' :=
-  Classical.choice (nonempty_linearEquiv_of_lift_dim_eq cond)
-#align linear_equiv.of_lift_dim_eq LinearEquiv.ofLiftDimEq
+  Classical.choice (nonempty_linearEquiv_of_lift_rank_eq cond)
+#align linear_equiv.of_lift_rank_eq LinearEquiv.ofLiftRankEq
 
 /-- Two vector spaces are isomorphic if they have the same dimension. -/
-def LinearEquiv.ofDimEq (cond : Module.rank K V = Module.rank K V₁) : V ≃ₗ[K] V₁ :=
-  Classical.choice (nonempty_linearEquiv_of_dim_eq cond)
-#align linear_equiv.of_dim_eq LinearEquiv.ofDimEq
+def LinearEquiv.ofRankEq (cond : Module.rank K V = Module.rank K V₁) : V ≃ₗ[K] V₁ :=
+  Classical.choice (nonempty_linearEquiv_of_rank_eq cond)
+#align linear_equiv.of_rank_eq LinearEquiv.ofRankEq
 
 end
 
 /-- Two vector spaces are isomorphic if and only if they have the same dimension. -/
-theorem LinearEquiv.nonempty_equiv_iff_lift_dim_eq :
+theorem LinearEquiv.nonempty_equiv_iff_lift_rank_eq :
     Nonempty (V ≃ₗ[K] V') ↔
       Cardinal.lift.{v'} (Module.rank K V) = Cardinal.lift.{v} (Module.rank K V') :=
-  ⟨fun ⟨h⟩ => LinearEquiv.lift_dim_eq h, fun h => nonempty_linearEquiv_of_lift_dim_eq h⟩
-#align linear_equiv.nonempty_equiv_iff_lift_dim_eq LinearEquiv.nonempty_equiv_iff_lift_dim_eq
+  ⟨fun ⟨h⟩ => LinearEquiv.lift_rank_eq h, fun h => nonempty_linearEquiv_of_lift_rank_eq h⟩
+#align linear_equiv.nonempty_equiv_iff_lift_rank_eq LinearEquiv.nonempty_equiv_iff_lift_rank_eq
 
 /-- Two vector spaces are isomorphic if and only if they have the same dimension. -/
-theorem LinearEquiv.nonempty_equiv_iff_dim_eq :
+theorem LinearEquiv.nonempty_equiv_iff_rank_eq :
     Nonempty (V ≃ₗ[K] V₁) ↔ Module.rank K V = Module.rank K V₁ :=
-  ⟨fun ⟨h⟩ => LinearEquiv.dim_eq h, fun h => nonempty_linearEquiv_of_dim_eq h⟩
-#align linear_equiv.nonempty_equiv_iff_dim_eq LinearEquiv.nonempty_equiv_iff_dim_eq
+  ⟨fun ⟨h⟩ => LinearEquiv.rank_eq h, fun h => nonempty_linearEquiv_of_rank_eq h⟩
+#align linear_equiv.nonempty_equiv_iff_rank_eq LinearEquiv.nonempty_equiv_iff_rank_eq
 
-theorem dim_prod : Module.rank K (V × V₁) = Module.rank K V + Module.rank K V₁ :=
+theorem rank_prod : Module.rank K (V × V₁) = Module.rank K V + Module.rank K V₁ :=
   by
   obtain ⟨⟨_, b⟩⟩ := Module.Free.exists_basis K V
   obtain ⟨⟨_, c⟩⟩ := Module.Free.exists_basis K V₁
-  rw [← Cardinal.lift_inj, ← (Basis.prod b c).mk_eq_dim, Cardinal.lift_add, ← Cardinal.mk_uLift, ←
-    b.mk_eq_dim, ← c.mk_eq_dim, ← Cardinal.mk_uLift, ← Cardinal.mk_uLift,
+  rw [← Cardinal.lift_inj, ← (Basis.prod b c).mk_eq_rank, Cardinal.lift_add, ← Cardinal.mk_uLift, ←
+    b.mk_eq_rank, ← c.mk_eq_rank, ← Cardinal.mk_uLift, ← Cardinal.mk_uLift,
     Cardinal.add_def (ULift _)]
   exact
     Cardinal.lift_inj.1
       (Cardinal.lift_mk_eq.2 ⟨equiv.ulift.trans (Equiv.sumCongr Equiv.ulift Equiv.ulift).symm⟩)
-#align dim_prod dim_prod
+#align rank_prod rank_prod
 
 section Fintype
 
@@ -1037,45 +1039,45 @@ variable [∀ i, AddCommGroup (φ i)] [∀ i, Module K (φ i)] [∀ i, Module.Fr
 
 open LinearMap
 
-theorem dim_pi [Finite η] : Module.rank K (∀ i, φ i) = Cardinal.sum fun i => Module.rank K (φ i) :=
+theorem rank_pi [Finite η] : Module.rank K (∀ i, φ i) = Cardinal.sum fun i => Module.rank K (φ i) :=
   by
   haveI := nontrivial_of_invariantBasisNumber K
   cases nonempty_fintype η
   let b i := (Module.Free.exists_basis K (φ i)).some.2
   let this : Basis (Σj, _) K (∀ j, φ j) := Pi.basis b
-  rw [← Cardinal.lift_inj, ← this.mk_eq_dim]
-  simp_rw [Cardinal.mk_sigma, Cardinal.lift_sum, ← (b _).mk_range_eq_dim,
+  rw [← Cardinal.lift_inj, ← this.mk_eq_rank]
+  simp_rw [Cardinal.mk_sigma, Cardinal.lift_sum, ← (b _).mk_range_eq_rank,
     Cardinal.mk_range_eq _ (b _).Injective]
-#align dim_pi dim_pi
+#align rank_pi rank_pi
 
 variable [Fintype η]
 
-theorem dim_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] [Module.Free K V] :
+theorem rank_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] [Module.Free K V] :
     Module.rank K (η → V) = Fintype.card η * Module.rank K V := by
-  rw [dim_pi, Cardinal.sum_const', Cardinal.mk_fintype]
-#align dim_fun dim_fun
+  rw [rank_pi, Cardinal.sum_const', Cardinal.mk_fintype]
+#align rank_fun rank_fun
 
-theorem dim_fun_eq_lift_mul :
+theorem rank_fun_eq_lift_mul :
     Module.rank K (η → V) =
       (Fintype.card η : Cardinal.{max u₁' v}) * Cardinal.lift.{u₁'} (Module.rank K V) :=
-  by rw [dim_pi, Cardinal.sum_const, Cardinal.mk_fintype, Cardinal.lift_natCast]
-#align dim_fun_eq_lift_mul dim_fun_eq_lift_mul
+  by rw [rank_pi, Cardinal.sum_const, Cardinal.mk_fintype, Cardinal.lift_natCast]
+#align rank_fun_eq_lift_mul rank_fun_eq_lift_mul
 
-theorem dim_fun' : Module.rank K (η → K) = Fintype.card η := by
-  rw [dim_fun_eq_lift_mul, dim_self, Cardinal.lift_one, mul_one, Cardinal.natCast_inj]
-#align dim_fun' dim_fun'
+theorem rank_fun' : Module.rank K (η → K) = Fintype.card η := by
+  rw [rank_fun_eq_lift_mul, rank_self, Cardinal.lift_one, mul_one, Cardinal.natCast_inj]
+#align rank_fun' rank_fun'
 
-theorem dim_fin_fun (n : ℕ) : Module.rank K (Fin n → K) = n := by simp [dim_fun']
-#align dim_fin_fun dim_fin_fun
+theorem rank_fin_fun (n : ℕ) : Module.rank K (Fin n → K) = n := by simp [rank_fun']
+#align rank_fin_fun rank_fin_fun
 
 end Fintype
 
-theorem Finsupp.dim_eq {ι : Type v} : Module.rank K (ι →₀ V) = (#ι) * Module.rank K V :=
+theorem Finsupp.rank_eq {ι : Type v} : Module.rank K (ι →₀ V) = (#ι) * Module.rank K V :=
   by
   obtain ⟨⟨_, bs⟩⟩ := Module.Free.exists_basis K V
-  rw [← bs.mk_eq_dim'', ← (Finsupp.basis fun a : ι => bs).mk_eq_dim'', Cardinal.mk_sigma,
+  rw [← bs.mk_eq_rank'', ← (Finsupp.basis fun a : ι => bs).mk_eq_rank'', Cardinal.mk_sigma,
     Cardinal.sum_const']
-#align finsupp.dim_eq Finsupp.dim_eq
+#align finsupp.rank_eq Finsupp.rank_eq
 
 -- TODO: merge with the `finrank` content
 /-- An `n`-dimensional `K`-vector space is equivalent to `fin n → K`. -/
@@ -1085,9 +1087,9 @@ def finDimVectorspaceEquiv (n : ℕ) (hn : Module.rank K V = n) : V ≃ₗ[K] Fi
   have : Cardinal.lift.{u} (n : Cardinal.{v}) = Cardinal.lift.{v} (n : Cardinal.{u}) := by simp
   have hn := Cardinal.lift_inj.{v, u}.2 hn
   rw [this] at hn
-  rw [← @dim_fin_fun K _ _ n] at hn
+  rw [← @rank_fin_fun K _ _ n] at hn
   haveI : Module.Free K (Fin n → K) := Module.Free.pi _ _
-  exact Classical.choice (nonempty_linearEquiv_of_lift_dim_eq hn)
+  exact Classical.choice (nonempty_linearEquiv_of_lift_rank_eq hn)
 #align fin_dim_vectorspace_equiv finDimVectorspaceEquiv
 
 end Free
@@ -1105,48 +1107,48 @@ variable [AddCommGroup V₁] [Module K V₁]
 variable {K V}
 
 /-- If a vector space has a finite dimension, the index set of `basis.of_vector_space` is finite. -/
-theorem Basis.finite_ofVectorSpaceIndex_of_dim_lt_aleph0 (h : Module.rank K V < ℵ₀) :
+theorem Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0 (h : Module.rank K V < ℵ₀) :
     (Basis.ofVectorSpaceIndex K V).Finite :=
-  finite_def.2 <| (Basis.ofVectorSpace K V).nonempty_fintype_index_of_dim_lt_aleph0 h
-#align basis.finite_of_vector_space_index_of_dim_lt_aleph_0 Basis.finite_ofVectorSpaceIndex_of_dim_lt_aleph0
+  finite_def.2 <| (Basis.ofVectorSpace K V).nonempty_fintype_index_of_rank_lt_aleph0 h
+#align basis.finite_of_vector_space_index_of_rank_lt_aleph_0 Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0
 
 -- TODO how far can we generalise this?
 -- When `s` is finite, we could prove this for any ring satisfying the strong rank condition
 -- using `linear_independent_le_span'`
-theorem dim_span_le (s : Set V) : Module.rank K (span K s) ≤ (#s) :=
+theorem rank_span_le (s : Set V) : Module.rank K (span K s) ≤ (#s) :=
   by
   obtain ⟨b, hb, hsab, hlib⟩ := exists_linearIndependent K s
   convert Cardinal.mk_le_mk_of_subset hb
-  rw [← hsab, dim_span_set hlib]
-#align dim_span_le dim_span_le
+  rw [← hsab, rank_span_set hlib]
+#align rank_span_le rank_span_le
 
-theorem dim_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V)) < ℵ₀ :=
+theorem rank_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V)) < ℵ₀ :=
   calc
-    Module.rank K (span K (↑s : Set V)) ≤ (#(↑s : Set V)) := dim_span_le ↑s
+    Module.rank K (span K (↑s : Set V)) ≤ (#(↑s : Set V)) := rank_span_le ↑s
     _ = s.card := by rw [Finset.coe_sort_coe, Cardinal.mk_coe_finset]
     _ < ℵ₀ := Cardinal.nat_lt_aleph0 _
     
-#align dim_span_of_finset dim_span_of_finset
+#align rank_span_of_finset rank_span_of_finset
 
-theorem dim_quotient_add_dim (p : Submodule K V) :
+theorem rank_quotient_add_rank (p : Submodule K V) :
     Module.rank K (V ⧸ p) + Module.rank K p = Module.rank K V := by
   classical exact
       let ⟨f⟩ := quotient_prod_linearEquiv p
-      dim_prod.symm.trans f.dim_eq
-#align dim_quotient_add_dim dim_quotient_add_dim
+      rank_prod.symm.trans f.rank_eq
+#align rank_quotient_add_rank rank_quotient_add_rank
 
 /-- rank-nullity theorem -/
-theorem dim_range_add_dim_ker (f : V →ₗ[K] V₁) :
+theorem rank_range_add_rank_ker (f : V →ₗ[K] V₁) :
     Module.rank K f.range + Module.rank K f.ker = Module.rank K V :=
   by
   haveI := fun p : Submodule K V => Classical.decEq (V ⧸ p)
-  rw [← f.quot_ker_equiv_range.dim_eq, dim_quotient_add_dim]
-#align dim_range_add_dim_ker dim_range_add_dim_ker
+  rw [← f.quot_ker_equiv_range.rank_eq, rank_quotient_add_rank]
+#align rank_range_add_rank_ker rank_range_add_rank_ker
 
-theorem dim_eq_of_surjective (f : V →ₗ[K] V₁) (h : Surjective f) :
+theorem rank_eq_of_surjective (f : V →ₗ[K] V₁) (h : Surjective f) :
     Module.rank K V = Module.rank K V₁ + Module.rank K f.ker := by
-  rw [← dim_range_add_dim_ker f, ← dim_range_of_surjective f h]
-#align dim_eq_of_surjective dim_eq_of_surjective
+  rw [← rank_range_add_rank_ker f, ← rank_range_of_surjective f h]
+#align rank_eq_of_surjective rank_eq_of_surjective
 
 section
 
@@ -1156,18 +1158,18 @@ variable [AddCommGroup V₃] [Module K V₃]
 
 open LinearMap
 
-/-- This is mostly an auxiliary lemma for `dim_sup_add_dim_inf_eq`. -/
-theorem dim_add_dim_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd : V₁ →ₗ[K] V₂) (ce : V₁ →ₗ[K] V₃)
-    (hde : ⊤ ≤ db.range ⊔ eb.range) (hgd : ker cd = ⊥) (eq : db.comp cd = eb.comp ce)
-    (eq₂ : ∀ d e, db d = eb e → ∃ c, cd c = d ∧ ce c = e) :
+/-- This is mostly an auxiliary lemma for `rank_sup_add_rank_inf_eq`. -/
+theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd : V₁ →ₗ[K] V₂)
+    (ce : V₁ →ₗ[K] V₃) (hde : ⊤ ≤ db.range ⊔ eb.range) (hgd : ker cd = ⊥)
+    (eq : db.comp cd = eb.comp ce) (eq₂ : ∀ d e, db d = eb e → ∃ c, cd c = d ∧ ce c = e) :
     Module.rank K V + Module.rank K V₁ = Module.rank K V₂ + Module.rank K V₃ :=
   by
   have hf : Surjective (coprod db eb) := by rwa [← range_eq_top, range_coprod, eq_top_iff]
   conv =>
     rhs
-    rw [← dim_prod, dim_eq_of_surjective _ hf]
+    rw [← rank_prod, rank_eq_of_surjective _ hf]
   congr 1
-  apply LinearEquiv.dim_eq
+  apply LinearEquiv.rank_eq
   refine' LinearEquiv.ofBijective _ ⟨_, _⟩
   · refine' cod_restrict _ (Prod cd (-ce)) _
     · intro c
@@ -1185,12 +1187,12 @@ theorem dim_add_dim_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd :
     rcases h hde with ⟨c, h₁, h₂⟩
     refine' ⟨c, h₁, _⟩
     rw [h₂, _root_.neg_neg]
-#align dim_add_dim_split dim_add_dim_split
+#align rank_add_rank_split rank_add_rank_split
 
-theorem dim_sup_add_dim_inf_eq (s t : Submodule K V) :
+theorem rank_sup_add_rank_inf_eq (s t : Submodule K V) :
     Module.rank K (s ⊔ t : Submodule K V) + Module.rank K (s ⊓ t : Submodule K V) =
       Module.rank K s + Module.rank K t :=
-  dim_add_dim_split (ofLe le_sup_left) (ofLe le_sup_right) (ofLe inf_le_left) (ofLe inf_le_right)
+  rank_add_rank_split (ofLe le_sup_left) (ofLe le_sup_right) (ofLe inf_le_left) (ofLe inf_le_right)
     (by
       rw [← map_le_map_iff' (ker_subtype <| s ⊔ t), Submodule.map_sup, Submodule.map_top, ←
         LinearMap.range_comp, ← LinearMap.range_comp, subtype_comp_of_le, subtype_comp_of_le,
@@ -1201,14 +1203,14 @@ theorem dim_sup_add_dim_inf_eq (s t : Submodule K V) :
       rintro ⟨b₁, hb₁⟩ ⟨b₂, hb₂⟩ eq
       obtain rfl : b₁ = b₂ := congr_arg Subtype.val Eq
       exact ⟨⟨b₁, hb₁, hb₂⟩, rfl, rfl⟩)
-#align dim_sup_add_dim_inf_eq dim_sup_add_dim_inf_eq
+#align rank_sup_add_rank_inf_eq rank_sup_add_rank_inf_eq
 
-theorem dim_add_le_dim_add_dim (s t : Submodule K V) :
+theorem rank_add_le_rank_add_rank (s t : Submodule K V) :
     Module.rank K (s ⊔ t : Submodule K V) ≤ Module.rank K s + Module.rank K t :=
   by
-  rw [← dim_sup_add_dim_inf_eq]
+  rw [← rank_sup_add_rank_inf_eq]
   exact self_le_add_right _ _
-#align dim_add_le_dim_add_dim dim_add_le_dim_add_dim
+#align rank_add_le_rank_add_rank rank_add_le_rank_add_rank
 
 end
 
@@ -1224,50 +1226,50 @@ variable [AddCommGroup V'] [Module K V']
 
 See also `finite_dimensional.fin_basis`.
 -/
-def Basis.ofDimEqZero {ι : Type _} [IsEmpty ι] (hV : Module.rank K V = 0) : Basis ι K V :=
-  haveI : Subsingleton V := dim_zero_iff.1 hV
+def Basis.ofRankEqZero {ι : Type _} [IsEmpty ι] (hV : Module.rank K V = 0) : Basis ι K V :=
+  haveI : Subsingleton V := rank_zero_iff.1 hV
   Basis.empty _
-#align basis.of_dim_eq_zero Basis.ofDimEqZero
+#align basis.of_rank_eq_zero Basis.ofRankEqZero
 
 @[simp]
-theorem Basis.ofDimEqZero_apply {ι : Type _} [IsEmpty ι] (hV : Module.rank K V = 0) (i : ι) :
-    Basis.ofDimEqZero hV i = 0 :=
+theorem Basis.ofRankEqZero_apply {ι : Type _} [IsEmpty ι] (hV : Module.rank K V = 0) (i : ι) :
+    Basis.ofRankEqZero hV i = 0 :=
   rfl
-#align basis.of_dim_eq_zero_apply Basis.ofDimEqZero_apply
+#align basis.of_rank_eq_zero_apply Basis.ofRankEqZero_apply
 
-theorem le_dim_iff_exists_linearIndependent {c : Cardinal} :
+theorem le_rank_iff_exists_linearIndependent {c : Cardinal} :
     c ≤ Module.rank K V ↔ ∃ s : Set V, (#s) = c ∧ LinearIndependent K (coe : s → V) :=
   by
   constructor
   · intro h
     let t := Basis.ofVectorSpace K V
-    rw [← t.mk_eq_dim'', Cardinal.le_mk_iff_exists_subset] at h
+    rw [← t.mk_eq_rank'', Cardinal.le_mk_iff_exists_subset] at h
     rcases h with ⟨s, hst, hsc⟩
     exact ⟨s, hsc, (of_vector_space_index.linear_independent K V).mono hst⟩
   · rintro ⟨s, rfl, si⟩
-    exact cardinal_le_dim_of_linearIndependent si
-#align le_dim_iff_exists_linear_independent le_dim_iff_exists_linearIndependent
+    exact cardinal_le_rank_of_linearIndependent si
+#align le_rank_iff_exists_linear_independent le_rank_iff_exists_linearIndependent
 
-theorem le_dim_iff_exists_linearIndependent_finset {n : ℕ} :
+theorem le_rank_iff_exists_linearIndependent_finset {n : ℕ} :
     ↑n ≤ Module.rank K V ↔
       ∃ s : Finset V, s.card = n ∧ LinearIndependent K (coe : (s : Set V) → V) :=
   by
-  simp only [le_dim_iff_exists_linearIndependent, Cardinal.mk_set_eq_nat_iff_finset]
+  simp only [le_rank_iff_exists_linearIndependent, Cardinal.mk_set_eq_nat_iff_finset]
   constructor
   · rintro ⟨s, ⟨t, rfl, rfl⟩, si⟩
     exact ⟨t, rfl, si⟩
   · rintro ⟨s, rfl, si⟩
     exact ⟨s, ⟨s, rfl, rfl⟩, si⟩
-#align le_dim_iff_exists_linear_independent_finset le_dim_iff_exists_linearIndependent_finset
+#align le_rank_iff_exists_linear_independent_finset le_rank_iff_exists_linearIndependent_finset
 
 /-- A vector space has dimension at most `1` if and only if there is a
 single vector of which all vectors are multiples. -/
-theorem dim_le_one_iff : Module.rank K V ≤ 1 ↔ ∃ v₀ : V, ∀ v, ∃ r : K, r • v₀ = v :=
+theorem rank_le_one_iff : Module.rank K V ≤ 1 ↔ ∃ v₀ : V, ∀ v, ∃ r : K, r • v₀ = v :=
   by
   let b := Basis.ofVectorSpace K V
   constructor
   · intro hd
-    rw [← b.mk_eq_dim'', Cardinal.le_one_iff_subsingleton, subsingleton_coe] at hd
+    rw [← b.mk_eq_rank'', Cardinal.le_one_iff_subsingleton, subsingleton_coe] at hd
     rcases eq_empty_or_nonempty (of_vector_space_index K V) with (hb | ⟨⟨v₀, hv₀⟩⟩)
     · use 0
       have h' : ∀ v : V, v = 0 := by simpa [hb, Submodule.eq_bot_iff] using b.span_eq.symm
@@ -1282,17 +1284,18 @@ theorem dim_le_one_iff : Module.rank K V ≤ 1 ↔ ∃ v₀ : V, ∀ v, ∃ r :
     have h : (K ∙ v₀) = ⊤ := by
       ext
       simp [mem_span_singleton, hv₀]
-    rw [← dim_top, ← h]
-    refine' (dim_span_le _).trans_eq _
+    rw [← rank_top, ← h]
+    refine' (rank_span_le _).trans_eq _
     simp
-#align dim_le_one_iff dim_le_one_iff
+#align rank_le_one_iff rank_le_one_iff
 
 /-- A submodule has dimension at most `1` if and only if there is a
 single vector in the submodule such that the submodule is contained in
 its span. -/
-theorem dim_submodule_le_one_iff (s : Submodule K V) : Module.rank K s ≤ 1 ↔ ∃ v₀ ∈ s, s ≤ K ∙ v₀ :=
+theorem rank_submodule_le_one_iff (s : Submodule K V) :
+    Module.rank K s ≤ 1 ↔ ∃ v₀ ∈ s, s ≤ K ∙ v₀ :=
   by
-  simp_rw [dim_le_one_iff, le_span_singleton_iff]
+  simp_rw [rank_le_one_iff, le_span_singleton_iff]
   constructor
   · rintro ⟨⟨v₀, hv₀⟩, h⟩
     use v₀, hv₀
@@ -1308,14 +1311,14 @@ theorem dim_submodule_le_one_iff (s : Submodule K V) : Module.rank K s ≤ 1 ↔
     use r
     simp_rw [Subtype.ext_iff, coe_smul, Submodule.coe_mk]
     exact hr
-#align dim_submodule_le_one_iff dim_submodule_le_one_iff
+#align rank_submodule_le_one_iff rank_submodule_le_one_iff
 
 /-- A submodule has dimension at most `1` if and only if there is a
 single vector, not necessarily in the submodule, such that the
 submodule is contained in its span. -/
-theorem dim_submodule_le_one_iff' (s : Submodule K V) : Module.rank K s ≤ 1 ↔ ∃ v₀, s ≤ K ∙ v₀ :=
+theorem rank_submodule_le_one_iff' (s : Submodule K V) : Module.rank K s ≤ 1 ↔ ∃ v₀, s ≤ K ∙ v₀ :=
   by
-  rw [dim_submodule_le_one_iff]
+  rw [rank_submodule_le_one_iff]
   constructor
   · rintro ⟨v₀, hv₀, h⟩
     exact ⟨v₀, h⟩
@@ -1331,12 +1334,12 @@ theorem dim_submodule_le_one_iff' (s : Submodule K V) : Module.rank K s ≤ 1 
     · push_neg  at hw
       rw [← Submodule.eq_bot_iff] at hw
       simp [hw]
-#align dim_submodule_le_one_iff' dim_submodule_le_one_iff'
+#align rank_submodule_le_one_iff' rank_submodule_le_one_iff'
 
 theorem Submodule.rank_le_one_iff_isPrincipal (W : Submodule K V) :
     Module.rank K W ≤ 1 ↔ W.IsPrincipal :=
   by
-  simp only [dim_le_one_iff, Submodule.isPrincipal_iff, le_antisymm_iff, le_span_singleton_iff,
+  simp only [rank_le_one_iff, Submodule.isPrincipal_iff, le_antisymm_iff, le_span_singleton_iff,
     span_singleton_le_iff_mem]
   constructor
   · rintro ⟨⟨m, hm⟩, hm'⟩
@@ -1349,7 +1352,7 @@ theorem Submodule.rank_le_one_iff_isPrincipal (W : Submodule K V) :
 
 theorem Module.rank_le_one_iff_top_isPrincipal :
     Module.rank K V ≤ 1 ↔ (⊤ : Submodule K V).IsPrincipal := by
-  rw [← Submodule.rank_le_one_iff_isPrincipal, dim_top]
+  rw [← Submodule.rank_le_one_iff_isPrincipal, rank_top]
 #align module.rank_le_one_iff_top_is_principal Module.rank_le_one_iff_top_isPrincipal
 
 end DivisionRing
@@ -1373,19 +1376,19 @@ def rank (f : V →ₗ[K] V') : Cardinal :=
 #align linear_map.rank LinearMap.rank
 
 theorem rank_le_range (f : V →ₗ[K] V₁) : rank f ≤ Module.rank K V₁ :=
-  dim_submodule_le _
+  rank_submodule_le _
 #align linear_map.rank_le_range LinearMap.rank_le_range
 
 @[simp]
 theorem rank_zero [Nontrivial K] : rank (0 : V →ₗ[K] V') = 0 := by
-  rw [rank, LinearMap.range_zero, dim_bot]
+  rw [rank, LinearMap.range_zero, rank_bot]
 #align linear_map.rank_zero LinearMap.rank_zero
 
 variable [AddCommGroup V''] [Module K V'']
 
 theorem rank_comp_le1 (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') : rank (f.comp g) ≤ rank f :=
   by
-  refine' dim_le_of_submodule _ _ _
+  refine' rank_le_of_submodule _ _ _
   rw [LinearMap.range_comp]
   exact LinearMap.map_le_range
 #align linear_map.rank_comp_le1 LinearMap.rank_comp_le1
@@ -1393,7 +1396,7 @@ theorem rank_comp_le1 (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') : rank (f.comp
 variable [AddCommGroup V'₁] [Module K V'₁]
 
 theorem rank_comp_le2 (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) : rank (f.comp g) ≤ rank g := by
-  rw [rank, rank, LinearMap.range_comp] <;> exact dim_map_le _ _
+  rw [rank, rank, LinearMap.range_comp] <;> exact rank_map_le _ _
 #align linear_map.rank_comp_le2 LinearMap.rank_comp_le2
 
 end Ring
@@ -1406,7 +1409,7 @@ variable [AddCommGroup V'] [Module K V']
 
 theorem rank_le_domain (f : V →ₗ[K] V₁) : rank f ≤ Module.rank K V :=
   by
-  rw [← dim_range_add_dim_ker f]
+  rw [← rank_range_add_rank_ker f]
   exact self_le_add_right _ _
 #align linear_map.rank_le_domain LinearMap.rank_le_domain
 
@@ -1414,13 +1417,13 @@ theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
   calc
     rank (f + g) ≤ Module.rank K (f.range ⊔ g.range : Submodule K V') :=
       by
-      refine' dim_le_of_submodule _ _ _
+      refine' rank_le_of_submodule _ _ _
       exact
         LinearMap.range_le_iff_comap.2 <|
           eq_top_iff'.2 fun x =>
             show f x + g x ∈ (f.range ⊔ g.range : Submodule K V') from
               mem_sup.2 ⟨_, ⟨x, rfl⟩, _, ⟨x, rfl⟩, rfl⟩
-    _ ≤ rank f + rank g := dim_add_le_dim_add_dim _ _
+    _ ≤ rank f + rank g := rank_add_le_rank_add_rank _ _
     
 #align linear_map.rank_add_le LinearMap.rank_add_le
 
@@ -1438,7 +1441,7 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'}
   rcases f.range_restrict.exists_right_inverse_of_surjective f.range_range_restrict with ⟨g, hg⟩
   have fg : left_inverse f.range_restrict g := LinearMap.congr_fun hg
   refine' ⟨fun h => _, _⟩
-  · rcases le_dim_iff_exists_linearIndependent.1 h with ⟨s, rfl, si⟩
+  · rcases le_rank_iff_exists_linearIndependent.1 h with ⟨s, rfl, si⟩
     refine' ⟨g '' s, Cardinal.mk_image_eq_lift _ _ fg.injective, _⟩
     replace fg : ∀ x, f (g x) = x
     · intro x
@@ -1449,7 +1452,7 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'}
   · rintro ⟨s, hsc, si⟩
     have : LinearIndependent K fun x : s => f.range_restrict x :=
       LinearIndependent.of_comp f.range.subtype (by convert si)
-    convert cardinal_le_dim_of_linearIndependent this.image
+    convert cardinal_le_rank_of_linearIndependent this.image
     rw [← Cardinal.lift_inj, ← hsc, Cardinal.mk_image_eq_of_injOn_lift]
     exact inj_on_iff_injective.2 this.injective
 #align linear_map.le_rank_iff_exists_linear_independent LinearMap.le_rank_iff_exists_linearIndependent
@@ -1457,7 +1460,7 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'}
 theorem le_rank_iff_exists_linearIndependent_finset {n : ℕ} {f : V →ₗ[K] V'} :
     ↑n ≤ rank f ↔ ∃ s : Finset V, s.card = n ∧ LinearIndependent K fun x : (s : Set V) => f x :=
   by
-  simp only [le_rank_iff_exists_linear_independent, Cardinal.lift_natCast, Cardinal.lift_eq_nat_iff,
+  simp only [le_rank_iff_exists_linearIndependent, Cardinal.lift_natCast, Cardinal.lift_eq_nat_iff,
     Cardinal.mk_set_eq_nat_iff_finset]
   constructor
   · rintro ⟨s, ⟨t, rfl, rfl⟩, si⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a4df69ca1a9a0e5e26bfe12e2b92814216016d0

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 
 ! This file was ported from Lean 3 source module linear_algebra.dimension
-! leanprover-community/mathlib commit 3cacc945118c8c637d89950af01da78307f59325
+! leanprover-community/mathlib commit be2ac64be57e8319fcd5c5547f3a8d9412daf5ec
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -486,7 +486,7 @@ theorem CompleteLattice.Independent.subtype_ne_bot_le_rank [NoZeroSMulDivisors R
 
 end
 
-section rank_zero
+section RankZero
 
 variable {R : Type u} {M : Type v}
 
@@ -552,7 +552,7 @@ theorem dim_pos_iff_nontrivial : 0 < Module.rank R M ↔ Nontrivial M :=
   dim_pos_iff_exists_ne_zero.trans (nontrivial_iff_exists_ne 0).symm
 #align dim_pos_iff_nontrivial dim_pos_iff_nontrivial
 
-end rank_zero
+end RankZero
 
 section InvariantBasisNumber
 
@@ -1037,9 +1037,9 @@ variable [∀ i, AddCommGroup (φ i)] [∀ i, Module K (φ i)] [∀ i, Module.Fr
 
 open LinearMap
 
-theorem dim_pi [Nontrivial K] [Finite η] :
-    Module.rank K (∀ i, φ i) = Cardinal.sum fun i => Module.rank K (φ i) :=
+theorem dim_pi [Finite η] : Module.rank K (∀ i, φ i) = Cardinal.sum fun i => Module.rank K (φ i) :=
   by
+  haveI := nontrivial_of_invariantBasisNumber K
   cases nonempty_fintype η
   let b i := (Module.Free.exists_basis K (φ i)).some.2
   let this : Basis (Σj, _) K (∀ j, φ j) := Pi.basis b
@@ -1050,22 +1050,22 @@ theorem dim_pi [Nontrivial K] [Finite η] :
 
 variable [Fintype η]
 
-theorem dim_fun {V η : Type u} [Nontrivial K] [Fintype η] [AddCommGroup V] [Module K V]
-    [Module.Free K V] : Module.rank K (η → V) = Fintype.card η * Module.rank K V := by
+theorem dim_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] [Module.Free K V] :
+    Module.rank K (η → V) = Fintype.card η * Module.rank K V := by
   rw [dim_pi, Cardinal.sum_const', Cardinal.mk_fintype]
 #align dim_fun dim_fun
 
-theorem dim_fun_eq_lift_mul [Nontrivial K] :
+theorem dim_fun_eq_lift_mul :
     Module.rank K (η → V) =
       (Fintype.card η : Cardinal.{max u₁' v}) * Cardinal.lift.{u₁'} (Module.rank K V) :=
   by rw [dim_pi, Cardinal.sum_const, Cardinal.mk_fintype, Cardinal.lift_natCast]
 #align dim_fun_eq_lift_mul dim_fun_eq_lift_mul
 
-theorem dim_fun' [Nontrivial K] : Module.rank K (η → K) = Fintype.card η := by
+theorem dim_fun' : Module.rank K (η → K) = Fintype.card η := by
   rw [dim_fun_eq_lift_mul, dim_self, Cardinal.lift_one, mul_one, Cardinal.natCast_inj]
 #align dim_fun' dim_fun'
 
-theorem dim_fin_fun [Nontrivial K] (n : ℕ) : Module.rank K (Fin n → K) = n := by simp [dim_fun']
+theorem dim_fin_fun (n : ℕ) : Module.rank K (Fin n → K) = n := by simp [dim_fun']
 #align dim_fin_fun dim_fin_fun
 
 end Fintype
@@ -1085,7 +1085,7 @@ def finDimVectorspaceEquiv (n : ℕ) (hn : Module.rank K V = n) : V ≃ₗ[K] Fi
   have : Cardinal.lift.{u} (n : Cardinal.{v}) = Cardinal.lift.{v} (n : Cardinal.{u}) := by simp
   have hn := Cardinal.lift_inj.{v, u}.2 hn
   rw [this] at hn
-  rw [← @dim_fin_fun K _ _ _ n] at hn
+  rw [← @dim_fin_fun K _ _ n] at hn
   haveI : Module.Free K (Fin n → K) := Module.Free.pi _ _
   exact Classical.choice (nonempty_linearEquiv_of_lift_dim_eq hn)
 #align fin_dim_vectorspace_equiv finDimVectorspaceEquiv
@@ -1214,79 +1214,12 @@ end
 
 end DivisionRing
 
-section rank
-
-section
-
-variable [Ring K] [AddCommGroup V] [Module K V] [AddCommGroup V₁] [Module K V₁]
-
-variable [AddCommGroup V'] [Module K V']
-
-/-- `rank f` is the rank of a `linear_map f`, defined as the dimension of `f.range`. -/
-def rank (f : V →ₗ[K] V') : Cardinal :=
-  Module.rank K f.range
-#align rank rank
-
-theorem rank_le_range (f : V →ₗ[K] V₁) : rank f ≤ Module.rank K V₁ :=
-  dim_submodule_le _
-#align rank_le_range rank_le_range
-
-@[simp]
-theorem rank_zero [Nontrivial K] : rank (0 : V →ₗ[K] V') = 0 := by
-  rw [rank, LinearMap.range_zero, dim_bot]
-#align rank_zero rank_zero
-
-variable [AddCommGroup V''] [Module K V'']
-
-theorem rank_comp_le1 (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') : rank (f.comp g) ≤ rank f :=
-  by
-  refine' dim_le_of_submodule _ _ _
-  rw [LinearMap.range_comp]
-  exact LinearMap.map_le_range
-#align rank_comp_le1 rank_comp_le1
-
-variable [AddCommGroup V'₁] [Module K V'₁]
-
-theorem rank_comp_le2 (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) : rank (f.comp g) ≤ rank g := by
-  rw [rank, rank, LinearMap.range_comp] <;> exact dim_map_le _ _
-#align rank_comp_le2 rank_comp_le2
-
-end
-
-end rank
-
 section DivisionRing
 
 variable [DivisionRing K] [AddCommGroup V] [Module K V] [AddCommGroup V₁] [Module K V₁]
 
 variable [AddCommGroup V'] [Module K V']
 
-theorem rank_le_domain (f : V →ₗ[K] V₁) : rank f ≤ Module.rank K V :=
-  by
-  rw [← dim_range_add_dim_ker f]
-  exact self_le_add_right _ _
-#align rank_le_domain rank_le_domain
-
-theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
-  calc
-    rank (f + g) ≤ Module.rank K (f.range ⊔ g.range : Submodule K V') :=
-      by
-      refine' dim_le_of_submodule _ _ _
-      exact
-        LinearMap.range_le_iff_comap.2 <|
-          eq_top_iff'.2 fun x =>
-            show f x + g x ∈ (f.range ⊔ g.range : Submodule K V') from
-              mem_sup.2 ⟨_, ⟨x, rfl⟩, _, ⟨x, rfl⟩, rfl⟩
-    _ ≤ rank f + rank g := dim_add_le_dim_add_dim _ _
-    
-#align rank_add_le rank_add_le
-
-theorem rank_finset_sum_le {η} (s : Finset η) (f : η → V →ₗ[K] V') :
-    rank (∑ d in s, f d) ≤ ∑ d in s, rank (f d) :=
-  @Finset.sum_hom_rel _ _ _ _ _ (fun a b => rank a ≤ b) f (fun d => rank (f d)) s
-    (le_of_eq rank_zero) fun i g c h => le_trans (rank_add_le _ _) (add_le_add_left h _)
-#align rank_finset_sum_le rank_finset_sum_le
-
 /-- The `ι` indexed basis on `V`, where `ι` is an empty type and `V` is zero-dimensional.
 
 See also `finite_dimensional.fin_basis`.
@@ -1419,6 +1352,84 @@ theorem Module.rank_le_one_iff_top_isPrincipal :
   rw [← Submodule.rank_le_one_iff_isPrincipal, dim_top]
 #align module.rank_le_one_iff_top_is_principal Module.rank_le_one_iff_top_isPrincipal
 
+end DivisionRing
+
+end Module
+
+/-! ### The rank of a linear map -/
+
+
+namespace LinearMap
+
+section Ring
+
+variable [Ring K] [AddCommGroup V] [Module K V] [AddCommGroup V₁] [Module K V₁]
+
+variable [AddCommGroup V'] [Module K V']
+
+/-- `rank f` is the rank of a `linear_map` `f`, defined as the dimension of `f.range`. -/
+def rank (f : V →ₗ[K] V') : Cardinal :=
+  Module.rank K f.range
+#align linear_map.rank LinearMap.rank
+
+theorem rank_le_range (f : V →ₗ[K] V₁) : rank f ≤ Module.rank K V₁ :=
+  dim_submodule_le _
+#align linear_map.rank_le_range LinearMap.rank_le_range
+
+@[simp]
+theorem rank_zero [Nontrivial K] : rank (0 : V →ₗ[K] V') = 0 := by
+  rw [rank, LinearMap.range_zero, dim_bot]
+#align linear_map.rank_zero LinearMap.rank_zero
+
+variable [AddCommGroup V''] [Module K V'']
+
+theorem rank_comp_le1 (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') : rank (f.comp g) ≤ rank f :=
+  by
+  refine' dim_le_of_submodule _ _ _
+  rw [LinearMap.range_comp]
+  exact LinearMap.map_le_range
+#align linear_map.rank_comp_le1 LinearMap.rank_comp_le1
+
+variable [AddCommGroup V'₁] [Module K V'₁]
+
+theorem rank_comp_le2 (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) : rank (f.comp g) ≤ rank g := by
+  rw [rank, rank, LinearMap.range_comp] <;> exact dim_map_le _ _
+#align linear_map.rank_comp_le2 LinearMap.rank_comp_le2
+
+end Ring
+
+section DivisionRing
+
+variable [DivisionRing K] [AddCommGroup V] [Module K V] [AddCommGroup V₁] [Module K V₁]
+
+variable [AddCommGroup V'] [Module K V']
+
+theorem rank_le_domain (f : V →ₗ[K] V₁) : rank f ≤ Module.rank K V :=
+  by
+  rw [← dim_range_add_dim_ker f]
+  exact self_le_add_right _ _
+#align linear_map.rank_le_domain LinearMap.rank_le_domain
+
+theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
+  calc
+    rank (f + g) ≤ Module.rank K (f.range ⊔ g.range : Submodule K V') :=
+      by
+      refine' dim_le_of_submodule _ _ _
+      exact
+        LinearMap.range_le_iff_comap.2 <|
+          eq_top_iff'.2 fun x =>
+            show f x + g x ∈ (f.range ⊔ g.range : Submodule K V') from
+              mem_sup.2 ⟨_, ⟨x, rfl⟩, _, ⟨x, rfl⟩, rfl⟩
+    _ ≤ rank f + rank g := dim_add_le_dim_add_dim _ _
+    
+#align linear_map.rank_add_le LinearMap.rank_add_le
+
+theorem rank_finset_sum_le {η} (s : Finset η) (f : η → V →ₗ[K] V') :
+    rank (∑ d in s, f d) ≤ ∑ d in s, rank (f d) :=
+  @Finset.sum_hom_rel _ _ _ _ _ (fun a b => rank a ≤ b) f (fun d => rank (f d)) s
+    (le_of_eq rank_zero) fun i g c h => le_trans (rank_add_le _ _) (add_le_add_left h _)
+#align linear_map.rank_finset_sum_le LinearMap.rank_finset_sum_le
+
 theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'} :
     c ≤ rank f ↔
       ∃ s : Set V,
@@ -1441,21 +1452,21 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'}
     convert cardinal_le_dim_of_linearIndependent this.image
     rw [← Cardinal.lift_inj, ← hsc, Cardinal.mk_image_eq_of_injOn_lift]
     exact inj_on_iff_injective.2 this.injective
-#align le_rank_iff_exists_linear_independent le_rank_iff_exists_linearIndependent
+#align linear_map.le_rank_iff_exists_linear_independent LinearMap.le_rank_iff_exists_linearIndependent
 
 theorem le_rank_iff_exists_linearIndependent_finset {n : ℕ} {f : V →ₗ[K] V'} :
     ↑n ≤ rank f ↔ ∃ s : Finset V, s.card = n ∧ LinearIndependent K fun x : (s : Set V) => f x :=
   by
-  simp only [le_rank_iff_exists_linearIndependent, Cardinal.lift_natCast, Cardinal.lift_eq_nat_iff,
+  simp only [le_rank_iff_exists_linear_independent, Cardinal.lift_natCast, Cardinal.lift_eq_nat_iff,
     Cardinal.mk_set_eq_nat_iff_finset]
   constructor
   · rintro ⟨s, ⟨t, rfl, rfl⟩, si⟩
     exact ⟨t, rfl, si⟩
   · rintro ⟨s, rfl, si⟩
     exact ⟨s, ⟨s, rfl, rfl⟩, si⟩
-#align le_rank_iff_exists_linear_independent_finset le_rank_iff_exists_linearIndependent_finset
+#align linear_map.le_rank_iff_exists_linear_independent_finset LinearMap.le_rank_iff_exists_linearIndependent_finset
 
 end DivisionRing
 
-end Module
+end LinearMap
 

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

@@ -4,12 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 
 ! This file was ported from Lean 3 source module linear_algebra.dimension
-! leanprover-community/mathlib commit 500ccb102e657148301f2ec059e8ee766b8660f3
+! leanprover-community/mathlib commit 3cacc945118c8c637d89950af01da78307f59325
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Module.BigOperators
 import Mathbin.LinearAlgebra.Dfinsupp
+import Mathbin.LinearAlgebra.FreeModule.Basic
 import Mathbin.LinearAlgebra.InvariantBasisNumber
 import Mathbin.LinearAlgebra.Isomorphisms
 import Mathbin.LinearAlgebra.StdBasis
@@ -305,6 +306,11 @@ theorem dim_bot : Module.rank R (⊥ : Submodule R M) = 0 :=
 
 variable {R M}
 
+theorem exists_mem_ne_zero_of_dim_pos {s : Submodule R M} (h : 0 < Module.rank R s) :
+    ∃ b : M, b ∈ s ∧ b ≠ 0 :=
+  exists_mem_ne_zero_of_ne_bot fun eq => by rw [Eq, dim_bot] at h <;> exact lt_irrefl _ h
+#align exists_mem_ne_zero_of_dim_pos exists_mem_ne_zero_of_dim_pos
+
 /-- A linearly-independent family of vectors in a module over a non-trivial ring must be finite if
 the module is Noetherian. -/
 theorem LinearIndependent.finite_of_isNoetherian [IsNoetherian R M] {v : ι → M}
@@ -952,26 +958,25 @@ theorem dim_self : Module.rank R R = 1 := by
 
 end StrongRankCondition
 
-section DivisionRing
+section Free
 
-variable [DivisionRing K] [AddCommGroup V] [Module K V] [AddCommGroup V₁] [Module K V₁]
+variable [Ring K] [StrongRankCondition K]
 
-variable {K V}
+variable [AddCommGroup V] [Module K V] [Module.Free K V]
 
-/-- If a vector space has a finite dimension, the index set of `basis.of_vector_space` is finite. -/
-theorem Basis.finite_ofVectorSpaceIndex_of_dim_lt_aleph0 (h : Module.rank K V < ℵ₀) :
-    (Basis.ofVectorSpaceIndex K V).Finite :=
-  finite_def.2 <| (Basis.ofVectorSpace K V).nonempty_fintype_index_of_dim_lt_aleph0 h
-#align basis.finite_of_vector_space_index_of_dim_lt_aleph_0 Basis.finite_ofVectorSpaceIndex_of_dim_lt_aleph0
+variable [AddCommGroup V'] [Module K V'] [Module.Free K V']
 
-variable [AddCommGroup V'] [Module K V']
+variable [AddCommGroup V₁] [Module K V₁] [Module.Free K V₁]
+
+variable {K V}
 
 /-- Two vector spaces are isomorphic if they have the same dimension. -/
 theorem nonempty_linearEquiv_of_lift_dim_eq
     (cond : Cardinal.lift.{v'} (Module.rank K V) = Cardinal.lift.{v} (Module.rank K V')) :
-    Nonempty (V ≃ₗ[K] V') := by
-  let B := Basis.ofVectorSpace K V
-  let B' := Basis.ofVectorSpace K V'
+    Nonempty (V ≃ₗ[K] V') :=
+  by
+  obtain ⟨⟨_, B⟩⟩ := Module.Free.exists_basis K V
+  obtain ⟨⟨_, B'⟩⟩ := Module.Free.exists_basis K V'
   have : Cardinal.lift.{v', v} (#_) = Cardinal.lift.{v, v'} (#_) := by
     rw [B.mk_eq_dim'', cond, B'.mk_eq_dim'']
   exact (Cardinal.lift_mk_eq.{v, v', 0}.1 this).map (B.equiv B')
@@ -1014,28 +1019,10 @@ theorem LinearEquiv.nonempty_equiv_iff_dim_eq :
   ⟨fun ⟨h⟩ => LinearEquiv.dim_eq h, fun h => nonempty_linearEquiv_of_dim_eq h⟩
 #align linear_equiv.nonempty_equiv_iff_dim_eq LinearEquiv.nonempty_equiv_iff_dim_eq
 
--- TODO how far can we generalise this?
--- When `s` is finite, we could prove this for any ring satisfying the strong rank condition
--- using `linear_independent_le_span'`
-theorem dim_span_le (s : Set V) : Module.rank K (span K s) ≤ (#s) :=
-  by
-  obtain ⟨b, hb, hsab, hlib⟩ := exists_linearIndependent K s
-  convert Cardinal.mk_le_mk_of_subset hb
-  rw [← hsab, dim_span_set hlib]
-#align dim_span_le dim_span_le
-
-theorem dim_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V)) < ℵ₀ :=
-  calc
-    Module.rank K (span K (↑s : Set V)) ≤ (#(↑s : Set V)) := dim_span_le ↑s
-    _ = s.card := by rw [Finset.coe_sort_coe, Cardinal.mk_coe_finset]
-    _ < ℵ₀ := Cardinal.nat_lt_aleph0 _
-    
-#align dim_span_of_finset dim_span_of_finset
-
 theorem dim_prod : Module.rank K (V × V₁) = Module.rank K V + Module.rank K V₁ :=
   by
-  let b := Basis.ofVectorSpace K V
-  let c := Basis.ofVectorSpace K V₁
+  obtain ⟨⟨_, b⟩⟩ := Module.Free.exists_basis K V
+  obtain ⟨⟨_, c⟩⟩ := Module.Free.exists_basis K V₁
   rw [← Cardinal.lift_inj, ← (Basis.prod b c).mk_eq_dim, Cardinal.lift_add, ← Cardinal.mk_uLift, ←
     b.mk_eq_dim, ← c.mk_eq_dim, ← Cardinal.mk_uLift, ← Cardinal.mk_uLift,
     Cardinal.add_def (ULift _)]
@@ -1046,41 +1033,101 @@ theorem dim_prod : Module.rank K (V × V₁) = Module.rank K V + Module.rank K V
 
 section Fintype
 
-variable [∀ i, AddCommGroup (φ i)] [∀ i, Module K (φ i)]
+variable [∀ i, AddCommGroup (φ i)] [∀ i, Module K (φ i)] [∀ i, Module.Free K (φ i)]
 
 open LinearMap
 
-theorem dim_pi [Finite η] : Module.rank K (∀ i, φ i) = Cardinal.sum fun i => Module.rank K (φ i) :=
+theorem dim_pi [Nontrivial K] [Finite η] :
+    Module.rank K (∀ i, φ i) = Cardinal.sum fun i => Module.rank K (φ i) :=
   by
   cases nonempty_fintype η
-  let b i := Basis.ofVectorSpace K (φ i)
+  let b i := (Module.Free.exists_basis K (φ i)).some.2
   let this : Basis (Σj, _) K (∀ j, φ j) := Pi.basis b
   rw [← Cardinal.lift_inj, ← this.mk_eq_dim]
-  simp [← (b _).mk_range_eq_dim]
+  simp_rw [Cardinal.mk_sigma, Cardinal.lift_sum, ← (b _).mk_range_eq_dim,
+    Cardinal.mk_range_eq _ (b _).Injective]
 #align dim_pi dim_pi
 
 variable [Fintype η]
 
-theorem dim_fun {V η : Type u} [Fintype η] [AddCommGroup V] [Module K V] :
-    Module.rank K (η → V) = Fintype.card η * Module.rank K V := by
+theorem dim_fun {V η : Type u} [Nontrivial K] [Fintype η] [AddCommGroup V] [Module K V]
+    [Module.Free K V] : Module.rank K (η → V) = Fintype.card η * Module.rank K V := by
   rw [dim_pi, Cardinal.sum_const', Cardinal.mk_fintype]
 #align dim_fun dim_fun
 
-theorem dim_fun_eq_lift_mul :
+theorem dim_fun_eq_lift_mul [Nontrivial K] :
     Module.rank K (η → V) =
       (Fintype.card η : Cardinal.{max u₁' v}) * Cardinal.lift.{u₁'} (Module.rank K V) :=
   by rw [dim_pi, Cardinal.sum_const, Cardinal.mk_fintype, Cardinal.lift_natCast]
 #align dim_fun_eq_lift_mul dim_fun_eq_lift_mul
 
-theorem dim_fun' : Module.rank K (η → K) = Fintype.card η := by
+theorem dim_fun' [Nontrivial K] : Module.rank K (η → K) = Fintype.card η := by
   rw [dim_fun_eq_lift_mul, dim_self, Cardinal.lift_one, mul_one, Cardinal.natCast_inj]
 #align dim_fun' dim_fun'
 
-theorem dim_fin_fun (n : ℕ) : Module.rank K (Fin n → K) = n := by simp [dim_fun']
+theorem dim_fin_fun [Nontrivial K] (n : ℕ) : Module.rank K (Fin n → K) = n := by simp [dim_fun']
 #align dim_fin_fun dim_fin_fun
 
 end Fintype
 
+theorem Finsupp.dim_eq {ι : Type v} : Module.rank K (ι →₀ V) = (#ι) * Module.rank K V :=
+  by
+  obtain ⟨⟨_, bs⟩⟩ := Module.Free.exists_basis K V
+  rw [← bs.mk_eq_dim'', ← (Finsupp.basis fun a : ι => bs).mk_eq_dim'', Cardinal.mk_sigma,
+    Cardinal.sum_const']
+#align finsupp.dim_eq Finsupp.dim_eq
+
+-- TODO: merge with the `finrank` content
+/-- An `n`-dimensional `K`-vector space is equivalent to `fin n → K`. -/
+def finDimVectorspaceEquiv (n : ℕ) (hn : Module.rank K V = n) : V ≃ₗ[K] Fin n → K :=
+  by
+  haveI := nontrivial_of_invariantBasisNumber K
+  have : Cardinal.lift.{u} (n : Cardinal.{v}) = Cardinal.lift.{v} (n : Cardinal.{u}) := by simp
+  have hn := Cardinal.lift_inj.{v, u}.2 hn
+  rw [this] at hn
+  rw [← @dim_fin_fun K _ _ _ n] at hn
+  haveI : Module.Free K (Fin n → K) := Module.Free.pi _ _
+  exact Classical.choice (nonempty_linearEquiv_of_lift_dim_eq hn)
+#align fin_dim_vectorspace_equiv finDimVectorspaceEquiv
+
+end Free
+
+section DivisionRing
+
+variable [DivisionRing K]
+
+variable [AddCommGroup V] [Module K V]
+
+variable [AddCommGroup V'] [Module K V']
+
+variable [AddCommGroup V₁] [Module K V₁]
+
+variable {K V}
+
+/-- If a vector space has a finite dimension, the index set of `basis.of_vector_space` is finite. -/
+theorem Basis.finite_ofVectorSpaceIndex_of_dim_lt_aleph0 (h : Module.rank K V < ℵ₀) :
+    (Basis.ofVectorSpaceIndex K V).Finite :=
+  finite_def.2 <| (Basis.ofVectorSpace K V).nonempty_fintype_index_of_dim_lt_aleph0 h
+#align basis.finite_of_vector_space_index_of_dim_lt_aleph_0 Basis.finite_ofVectorSpaceIndex_of_dim_lt_aleph0
+
+-- TODO how far can we generalise this?
+-- When `s` is finite, we could prove this for any ring satisfying the strong rank condition
+-- using `linear_independent_le_span'`
+theorem dim_span_le (s : Set V) : Module.rank K (span K s) ≤ (#s) :=
+  by
+  obtain ⟨b, hb, hsab, hlib⟩ := exists_linearIndependent K s
+  convert Cardinal.mk_le_mk_of_subset hb
+  rw [← hsab, dim_span_set hlib]
+#align dim_span_le dim_span_le
+
+theorem dim_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V)) < ℵ₀ :=
+  calc
+    Module.rank K (span K (↑s : Set V)) ≤ (#(↑s : Set V)) := dim_span_le ↑s
+    _ = s.card := by rw [Finset.coe_sort_coe, Cardinal.mk_coe_finset]
+    _ < ℵ₀ := Cardinal.nat_lt_aleph0 _
+    
+#align dim_span_of_finset dim_span_of_finset
+
 theorem dim_quotient_add_dim (p : Submodule K V) :
     Module.rank K (V ⧸ p) + Module.rank K p = Module.rank K V := by
   classical exact
@@ -1165,11 +1212,6 @@ theorem dim_add_le_dim_add_dim (s t : Submodule K V) :
 
 end
 
-theorem exists_mem_ne_zero_of_dim_pos {s : Submodule K V} (h : 0 < Module.rank K s) :
-    ∃ b : V, b ∈ s ∧ b ≠ 0 :=
-  exists_mem_ne_zero_of_ne_bot fun eq => by rw [Eq, dim_bot] at h <;> exact lt_irrefl _ h
-#align exists_mem_ne_zero_of_dim_pos exists_mem_ne_zero_of_dim_pos
-
 end DivisionRing
 
 section rank
@@ -1308,7 +1350,7 @@ theorem dim_le_one_iff : Module.rank K V ≤ 1 ↔ ∃ v₀ : V, ∀ v, ∃ r :
       ext
       simp [mem_span_singleton, hv₀]
     rw [← dim_top, ← h]
-    convert dim_span_le _
+    refine' (dim_span_le _).trans_eq _
     simp
 #align dim_le_one_iff dim_le_one_iff
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/d95bef0d215ea58c0fd7bbc4b151bf3fe952c095

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 
 ! This file was ported from Lean 3 source module linear_algebra.dimension
-! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
+! leanprover-community/mathlib commit 500ccb102e657148301f2ec059e8ee766b8660f3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -484,25 +484,54 @@ section rank_zero
 
 variable {R : Type u} {M : Type v}
 
-variable [Ring R] [Nontrivial R] [AddCommGroup M] [Module R M] [NoZeroSMulDivisors R M]
+variable [Ring R] [AddCommGroup M] [Module R M]
+
+@[simp]
+theorem dim_subsingleton [Subsingleton R] : Module.rank R M = 1 :=
+  by
+  haveI := Module.subsingleton R M
+  have : Nonempty { s : Set M // LinearIndependent R (coe : s → M) } :=
+    ⟨⟨∅, linearIndependent_empty _ _⟩⟩
+  rw [Module.rank, csupᵢ_eq_of_forall_le_of_forall_lt_exists_gt]
+  · rintro ⟨s, hs⟩
+    rw [Cardinal.mk_le_one_iff_set_subsingleton]
+    apply subsingleton_of_subsingleton
+  intro w hw
+  refine' ⟨⟨{0}, _⟩, _⟩
+  · rw [linearIndependent_iff']
+    intros
+    exact Subsingleton.elim _ _
+  · exact hw.trans_eq (Cardinal.mk_singleton _).symm
+#align dim_subsingleton dim_subsingleton
+
+variable [NoZeroSMulDivisors R M]
+
+theorem dim_pos [Nontrivial M] : 0 < Module.rank R M :=
+  by
+  obtain ⟨x, hx⟩ := exists_ne (0 : M)
+  suffices 1 ≤ Module.rank R M by exact zero_lt_one.trans_le this
+  letI := Module.nontrivial R M
+  suffices LinearIndependent R fun y : ({x} : Set M) => ↑y by
+    simpa using cardinal_le_dim_of_linearIndependent this
+  exact linearIndependent_singleton hx
+#align dim_pos dim_pos
+
+variable [Nontrivial R]
 
 theorem dim_zero_iff_forall_zero : Module.rank R M = 0 ↔ ∀ x : M, x = 0 :=
   by
   refine' ⟨fun h => _, fun h => _⟩
   · contrapose! h
     obtain ⟨x, hx⟩ := h
-    suffices 1 ≤ Module.rank R M by
-      intro h
-      exact this.not_lt (h.symm ▸ zero_lt_one)
-    suffices LinearIndependent R fun y : ({x} : Set M) => ↑y by
-      simpa using cardinal_le_dim_of_linearIndependent this
-    exact linearIndependent_singleton hx
+    letI : Nontrivial M := nontrivial_of_ne _ _ hx
+    exact dim_pos.ne'
   · have : (⊤ : Submodule R M) = ⊥ := by
       ext x
       simp [h x]
     rw [← dim_top, this, dim_bot]
 #align dim_zero_iff_forall_zero dim_zero_iff_forall_zero
 
+/-- See `dim_subsingleton` for the reason that `nontrivial R` is needed. -/
 theorem dim_zero_iff : Module.rank R M = 0 ↔ Subsingleton M :=
   dim_zero_iff_forall_zero.trans (subsingleton_iff_forall_eq 0).symm
 #align dim_zero_iff dim_zero_iff
@@ -517,10 +546,6 @@ theorem dim_pos_iff_nontrivial : 0 < Module.rank R M ↔ Nontrivial M :=
   dim_pos_iff_exists_ne_zero.trans (nontrivial_iff_exists_ne 0).symm
 #align dim_pos_iff_nontrivial dim_pos_iff_nontrivial
 
-theorem dim_pos [h : Nontrivial M] : 0 < Module.rank R M :=
-  dim_pos_iff_nontrivial.2 h
-#align dim_pos dim_pos
-
 end rank_zero
 
 section InvariantBasisNumber

mathlib commit https://github.com/leanprover-community/mathlib/commit/dd6388c44e6f6b4547070b887c5905d5cfe6c9f8

@@ -543,7 +543,7 @@ theorem mk_eq_mk_of_basis (v : Basis ι R M) (v' : Basis ι' R M) :
     rw [Cardinal.mk_fintype, Cardinal.mk_fintype]
     simp only [Cardinal.lift_natCast, Cardinal.natCast_inj]
     -- Now we can use invariant basis number to show they have the same cardinality.
-    apply card_eq_of_lequiv R
+    apply card_eq_of_linearEquiv R
     exact
       (Finsupp.linearEquivFunOnFinite R R ι).symm.trans v.repr.symm ≪≫ₗ v'.repr ≪≫ₗ
         Finsupp.linearEquivFunOnFinite R R ι'

mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 
 ! This file was ported from Lean 3 source module linear_algebra.dimension
-! leanprover-community/mathlib commit 2bbc7e3884ba234309d2a43b19144105a753292e
+! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -416,7 +416,7 @@ theorem union_support_maximal_linearIndependent_eq_range_basis {ι : Type w} (b
     -- by expressing the `v i` in the basis `b`, and using that the `v i` have no `b b'` term.
     have l₀ : l none = 0 := by
       rw [← eq_neg_iff_add_eq_zero] at z
-      replace z := eq_neg_of_eq_neg z
+      replace z := neg_eq_iff_eq_neg.mpr z
       apply_fun fun x => b.repr x b'  at z
       simp only [repr_self, LinearEquiv.map_smul, mul_one, Finsupp.single_eq_same, Pi.neg_apply,
         Finsupp.smul_single', LinearEquiv.map_neg, Finsupp.coe_neg] at z

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

A PR analogous to #12338 and #12361: reformatting proofs following the multiple goals linter of #12339.

@@ -113,7 +113,7 @@ theorem Basis.le_span'' {ι : Type*} [Fintype ι] (b : Basis ι R M) {w : Set M}
   fapply card_le_of_surjective' R
   · exact b.repr.toLinearMap.comp (Finsupp.total w M R (↑))
   · apply Surjective.comp (g := b.repr.toLinearMap)
-    apply LinearEquiv.surjective
+    · apply LinearEquiv.surjective
     rw [← LinearMap.range_eq_top, Finsupp.range_total]
     simpa using s
 #align basis.le_span'' Basis.le_span''

We define the coroots of a finite-dimensional semisimple Lie algebra with coefficients in a field characteristic zero and establish the key property that a coroot is complementary to the kernel of the root.

In addition we carry out some related, light refactoring. The most important points are:

• Promote LieModule.weight from a subtype to a structure LieModule.Weight + expand its API (we need this expanded API for the headline results).
• Replace the definition LieAlgebra.rootSpaceProductNegSelf with its range which we call LieAlgebra.corootSpace (in all places where we used this definition, it was the range that we actually used).
• Drop the very old (unused) definitions LieAlgebra.IsRoot and LieModule.IsWeight.

@@ -484,6 +484,12 @@ theorem Submodule.finrank_eq_zero [StrongRankCondition R] [NoZeroSMulDivisors R
   rw [← Submodule.rank_eq_zero, ← finrank_eq_rank, ← @Nat.cast_zero Cardinal, Cardinal.natCast_inj]
 #align finrank_eq_zero Submodule.finrank_eq_zero
 
+@[simp]
+lemma Submodule.one_le_finrank_iff [StrongRankCondition R] [NoZeroSMulDivisors R M]
+    {S : Submodule R M} [Module.Finite R S] :
+    1 ≤ finrank R S ↔ S ≠ ⊥ := by
+  simp [← not_iff_not]
+
 variable [Module.Free R M]
 
 theorem finrank_eq_zero_of_basis_imp_not_finite

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

@@ -265,7 +265,7 @@ theorem linearIndependent_of_top_le_span_of_card_eq_finrank {ι : Type*} [Fintyp
           rw [Set.toFinset_card, Fintype.card_ofFinset]
         _ ≤ (Set.univ \ {i}).toFinset.card := Finset.card_image_le
         _ = (Finset.univ.erase i).card := (congr_arg Finset.card (Finset.ext (by simp [and_comm])))
-        _ < Finset.univ.card := (Finset.card_erase_lt_of_mem (Finset.mem_univ i))
+        _ < Finset.univ.card := Finset.card_erase_lt_of_mem (Finset.mem_univ i)
         _ = finrank K V := card_eq
     -- We already have that `b '' univ` spans the whole space,
     -- so we only need to show that the span of `b '' (univ \ {i})` contains each `b j`.
@@ -290,7 +290,7 @@ theorem linearIndependent_of_top_le_span_of_card_eq_finrank {ι : Type*} [Fintyp
       (b i + (g i)⁻¹ • (s.erase i).sum fun j => g j • b j) =
           (g i)⁻¹ • (g i • b i + (s.erase i).sum fun j => g j • b j) :=
         by rw [smul_add, ← mul_smul, inv_mul_cancel gx_ne_zero, one_smul]
-      _ = (g i)⁻¹ • (0 : V) := (congr_arg _ ?_)
+      _ = (g i)⁻¹ • (0 : V) := congr_arg _ ?_
       _ = 0 := smul_zero _
     -- And then it's just a bit of manipulation with finite sums.
     rwa [← Finset.insert_erase i_mem_s, Finset.sum_insert (Finset.not_mem_erase _ _)] at dependent

Added a class HasRankNullity consisting of the rings that satisfy the rank-nullity theorem. Generalized the corollaries of the rank-nullity theorem from division rings to rings satisfying the class, and moved them into a new file LinearAlgebra.Dimension.RankNullity.

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

@@ -211,6 +211,54 @@ alias finset_card_le_finrank_of_linearIndependent := LinearIndependent.finset_ca
 @[deprecated]
 alias Module.Finite.lt_aleph0_of_linearIndependent := LinearIndependent.lt_aleph0_of_finite
 
+lemma exists_set_linearIndependent_of_lt_rank {n : Cardinal} (hn : n < Module.rank R M) :
+    ∃ s : Set M, #s = n ∧ LinearIndependent R ((↑) : s → M) := by
+  obtain ⟨⟨s, hs⟩, hs'⟩ := exists_lt_of_lt_ciSup' (hn.trans_eq (Module.rank_def R M))
+  obtain ⟨t, ht, ht'⟩ := le_mk_iff_exists_subset.mp hs'.le
+  exact ⟨t, ht', .mono ht hs⟩
+
+lemma exists_finset_linearIndependent_of_le_rank {n : ℕ} (hn : n ≤ Module.rank R M) :
+    ∃ s : Finset M, s.card = n ∧ LinearIndependent R ((↑) : s → M) := by
+  have := nonempty_linearIndependent_set
+  cases' hn.eq_or_lt with h h
+  · obtain ⟨⟨s, hs⟩, hs'⟩ := Cardinal.exists_eq_natCast_of_iSup_eq _
+      (Cardinal.bddAbove_range.{v, v} _) _ (h.trans (Module.rank_def R M)).symm
+    have : Finite s := lt_aleph0_iff_finite.mp (hs' ▸ nat_lt_aleph0 n)
+    cases nonempty_fintype s
+    exact ⟨s.toFinset, by simpa using hs', by convert hs <;> exact Set.mem_toFinset⟩
+  · obtain ⟨s, hs, hs'⟩ := exists_set_linearIndependent_of_lt_rank h
+    have : Finite s := lt_aleph0_iff_finite.mp (hs ▸ nat_lt_aleph0 n)
+    cases nonempty_fintype s
+    exact ⟨s.toFinset, by simpa using hs, by convert hs' <;> exact Set.mem_toFinset⟩
+
+lemma exists_linearIndependent_of_le_rank {n : ℕ} (hn : n ≤ Module.rank R M) :
+    ∃ f : Fin n → M, LinearIndependent R f :=
+  have ⟨_, hs, hs'⟩ := exists_finset_linearIndependent_of_le_rank hn
+  ⟨_, (linearIndependent_equiv (Finset.equivFinOfCardEq hs).symm).mpr hs'⟩
+
+lemma natCast_le_rank_iff {n : ℕ} :
+    n ≤ Module.rank R M ↔ ∃ f : Fin n → M, LinearIndependent R f :=
+  ⟨exists_linearIndependent_of_le_rank,
+    fun H ↦ by simpa using H.choose_spec.cardinal_lift_le_rank⟩
+
+lemma natCast_le_rank_iff_finset {n : ℕ} :
+    n ≤ Module.rank R M ↔ ∃ s : Finset M, s.card = n ∧ LinearIndependent R ((↑) : s → M) :=
+  ⟨exists_finset_linearIndependent_of_le_rank,
+    fun ⟨s, h₁, h₂⟩ ↦ by simpa [h₁] using h₂.cardinal_le_rank⟩
+
+lemma exists_finset_linearIndependent_of_le_finrank {n : ℕ} (hn : n ≤ finrank R M) :
+    ∃ s : Finset M, s.card = n ∧ LinearIndependent R ((↑) : s → M) := by
+  by_cases h : finrank R M = 0
+  · rw [le_zero_iff.mp (hn.trans_eq h)]
+    exact ⟨∅, rfl, by convert linearIndependent_empty R M using 2 <;> aesop⟩
+  exact exists_finset_linearIndependent_of_le_rank
+    ((natCast_le.mpr hn).trans_eq (cast_toNat_of_lt_aleph0 (toNat_ne_zero.mp h).2))
+
+lemma exists_linearIndependent_of_le_finrank {n : ℕ} (hn : n ≤ finrank R M) :
+    ∃ f : Fin n → M, LinearIndependent R f :=
+  have ⟨_, hs, hs'⟩ := exists_finset_linearIndependent_of_le_finrank hn
+  ⟨_, (linearIndependent_equiv (Finset.equivFinOfCardEq hs).symm).mpr hs'⟩
+
 variable [Module.Finite R M]
 
 theorem Module.Finite.not_linearIndependent_of_infinite {ι : Type*} [Infinite ι]

Added a class HasRankNullity consisting of the rings that satisfy the rank-nullity theorem. Generalized the corollaries of the rank-nullity theorem from division rings to rings satisfying the class, and moved them into a new file LinearAlgebra.Dimension.RankNullity.

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

@@ -7,7 +7,7 @@ Scott Morrison, Chris Hughes, Anne Baanen, Junyan Xu
 import Mathlib.LinearAlgebra.Basis.VectorSpace
 import Mathlib.LinearAlgebra.Dimension.Finite
 import Mathlib.SetTheory.Cardinal.Subfield
-import Mathlib.LinearAlgebra.Dimension.Constructions
+import Mathlib.LinearAlgebra.Dimension.RankNullity
 
 #align_import linear_algebra.dimension from "leanprover-community/mathlib"@"47a5f8186becdbc826190ced4312f8199f9db6a5"
 
@@ -21,7 +21,7 @@ over division rings.
 
 For vector spaces (i.e. modules over a field), we have
 
-* `rank_quotient_add_rank`: if `V₁` is a submodule of `V`, then
+* `rank_quotient_add_rank_of_divisionRing`: if `V₁` is a submodule of `V`, then
   `Module.rank (V/V₁) + Module.rank V₁ = Module.rank V`.
 * `rank_range_add_rank_ker`: the rank-nullity theorem.
 * `rank_dual_eq_card_dual_of_aleph0_le_rank`: The **Erdős-Kaplansky Theorem** which says that
@@ -33,7 +33,7 @@ For vector spaces (i.e. modules over a field), we have
 
 noncomputable section
 
-universe u v v' v'' u₁' w w'
+universe u₀ u v v' v'' u₁' w w'
 
 variable {K R : Type u} {V V₁ V₂ V₃ : Type v} {V' V'₁ : Type v'} {V'' : Type v''}
 variable {ι : Type w} {ι' : Type w'} {η : Type u₁'} {φ : η → Type*}
@@ -55,60 +55,20 @@ theorem Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0 (h : Module.rank K V <
   finite_def.2 <| (Basis.ofVectorSpace K V).nonempty_fintype_index_of_rank_lt_aleph0 h
 #align basis.finite_of_vector_space_index_of_rank_lt_aleph_0 Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0
 
-theorem rank_quotient_add_rank (p : Submodule K V) :
+/-- Also see `rank_quotient_add_rank`. -/
+theorem rank_quotient_add_rank_of_divisionRing (p : Submodule K V) :
     Module.rank K (V ⧸ p) + Module.rank K p = Module.rank K V := by
   classical
     let ⟨f⟩ := quotient_prod_linearEquiv p
     exact rank_prod'.symm.trans f.rank_eq
-#align rank_quotient_add_rank rank_quotient_add_rank
-
-/-- The **rank-nullity theorem** -/
-theorem rank_range_add_rank_ker (f : V →ₗ[K] V₁) :
-    Module.rank K (LinearMap.range f) + Module.rank K (LinearMap.ker f) = Module.rank K V := by
-  haveI := fun p : Submodule K V => Classical.decEq (V ⧸ p)
-  rw [← f.quotKerEquivRange.rank_eq, rank_quotient_add_rank]
-#align rank_range_add_rank_ker rank_range_add_rank_ker
-
-theorem rank_eq_of_surjective (f : V →ₗ[K] V₁) (h : Surjective f) :
-    Module.rank K V = Module.rank K V₁ + Module.rank K (LinearMap.ker f) := by
-  rw [← rank_range_add_rank_ker f, ← rank_range_of_surjective f h]
-#align rank_eq_of_surjective rank_eq_of_surjective
-
-/-- Given a family of `n` linearly independent vectors in a space of dimension `> n`, one may extend
-the family by another vector while retaining linear independence. -/
-theorem exists_linearIndependent_cons_of_lt_rank {n : ℕ} {v : Fin n → V}
-    (hv : LinearIndependent K v) (h : n < Module.rank K V) :
-    ∃ (x : V), LinearIndependent K (Fin.cons x v) := by
-  have A : Submodule.span K (range v) ≠ ⊤ := by
-    intro H
-    rw [← rank_top, ← H] at h
-    have : Module.rank K (Submodule.span K (range v)) ≤ n := by
-      have := Cardinal.mk_range_le_lift (f := v)
-      simp only [Cardinal.lift_id'] at this
-      exact (rank_span_le _).trans (this.trans (by simp))
-    exact lt_irrefl _ (h.trans_le this)
-  obtain ⟨x, hx⟩ : ∃ x, x ∉ Submodule.span K (range v) := by
-    contrapose! A
-    exact Iff.mpr Submodule.eq_top_iff' A
-  exact ⟨x, linearIndependent_fin_cons.2 ⟨hv, hx⟩⟩
-
-/-- Given a family of `n` linearly independent vectors in a space of dimension `> n`, one may extend
-the family by another vector while retaining linear independence. -/
-theorem exists_linearIndependent_snoc_of_lt_rank {n : ℕ} {v : Fin n → V}
-    (hv : LinearIndependent K v) (h : n < Module.rank K V) :
-    ∃ (x : V), LinearIndependent K (Fin.snoc v x) := by
-  simpa [linearIndependent_fin_cons, ← linearIndependent_fin_snoc]
-    using exists_linearIndependent_cons_of_lt_rank hv h
-
-/-- Given a nonzero vector in a space of dimension `> 1`, one may find another vector linearly
-independent of the first one. -/
-theorem exists_linearIndependent_pair_of_one_lt_rank
-    (h : 1 < Module.rank K V) {x : V} (hx : x ≠ 0) :
-    ∃ y, LinearIndependent K ![x, y] := by
-  obtain ⟨y, hy⟩ := exists_linearIndependent_snoc_of_lt_rank (linearIndependent_unique ![x] hx) h
-  have : Fin.snoc ![x] y = ![x, y] := Iff.mp List.ofFn_inj rfl
-  rw [this] at hy
-  exact ⟨y, hy⟩
+
+instance DivisionRing.hasRankNullity : HasRankNullity.{u₀} K where
+  rank_quotient_add_rank := rank_quotient_add_rank_of_divisionRing
+  exists_set_linearIndependent V _ _ := by
+    let b := Module.Free.chooseBasis K V
+    refine ⟨range b, ?_, b.linearIndependent.to_subtype_range⟩
+    rw [← lift_injective.eq_iff, mk_range_eq_of_injective b.injective,
+      Module.Free.rank_eq_card_chooseBasisIndex]
 
 section
 
@@ -125,7 +85,7 @@ theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd
   have hf : Surjective (coprod db eb) := by rwa [← range_eq_top, range_coprod, eq_top_iff]
   conv =>
     rhs
-    rw [← rank_prod', rank_eq_of_surjective _ hf]
+    rw [← rank_prod', rank_eq_of_surjective hf]
   congr 1
   apply LinearEquiv.rank_eq
   let L : V₁ →ₗ[K] ker (coprod db eb) := by -- Porting note: this is needed to avoid a timeout
@@ -148,29 +108,6 @@ theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd
     rw [h₂, _root_.neg_neg]
 #align rank_add_rank_split rank_add_rank_split
 
-theorem Submodule.rank_sup_add_rank_inf_eq (s t : Submodule K V) :
-    Module.rank K (s ⊔ t : Submodule K V) + Module.rank K (s ⊓ t : Submodule K V) =
-    Module.rank K s + Module.rank K t :=
-  rank_add_rank_split
-    (inclusion le_sup_left) (inclusion le_sup_right)
-    (inclusion inf_le_left) (inclusion inf_le_right)
-    (by
-      rw [← map_le_map_iff' (ker_subtype <| s ⊔ t), Submodule.map_sup, Submodule.map_top, ←
-        LinearMap.range_comp, ← LinearMap.range_comp, subtype_comp_inclusion,
-        subtype_comp_inclusion, range_subtype, range_subtype, range_subtype])
-    (ker_inclusion _ _ _) (by ext ⟨x, hx⟩; rfl)
-    (by
-      rintro ⟨b₁, hb₁⟩ ⟨b₂, hb₂⟩ eq
-      obtain rfl : b₁ = b₂ := congr_arg Subtype.val eq
-      exact ⟨⟨b₁, hb₁, hb₂⟩, rfl, rfl⟩)
-#align submodule.rank_sup_add_rank_inf_eq Submodule.rank_sup_add_rank_inf_eq
-
-theorem Submodule.rank_add_le_rank_add_rank (s t : Submodule K V) :
-    Module.rank K (s ⊔ t : Submodule K V) ≤ Module.rank K s + Module.rank K t := by
-  rw [← Submodule.rank_sup_add_rank_inf_eq]
-  exact self_le_add_right _ _
-#align submodule.rank_add_le_rank_add_rank Submodule.rank_add_le_rank_add_rank
-
 end
 
 end DivisionRing
@@ -307,35 +244,6 @@ theorem Module.rank_le_one_iff_top_isPrincipal :
 
 end Module
 
-section Span
-
-open Submodule FiniteDimensional
-
-variable [DivisionRing K] [AddCommGroup V] [Module K V]
-
-/-- Given a family of `n` linearly independent vectors in a finite-dimensional space of
-dimension `> n`, one may extend the family by another vector while retaining linear independence. -/
-theorem exists_linearIndependent_snoc_of_lt_finrank {n : ℕ} {v : Fin n → V}
-    (hv : LinearIndependent K v) (h : n < finrank K V) :
-    ∃ (x : V), LinearIndependent K (Fin.snoc v x) :=
-  exists_linearIndependent_snoc_of_lt_rank hv (lt_rank_of_lt_finrank h)
-
-/-- Given a family of `n` linearly independent vectors in a finite-dimensional space of
-dimension `> n`, one may extend the family by another vector while retaining linear independence. -/
-theorem exists_linearIndependent_cons_of_lt_finrank {n : ℕ} {v : Fin n → V}
-    (hv : LinearIndependent K v) (h : n < finrank K V) :
-    ∃ (x : V), LinearIndependent K (Fin.cons x v) :=
-  exists_linearIndependent_cons_of_lt_rank hv (lt_rank_of_lt_finrank h)
-
-/-- Given a nonzero vector in a finite-dimensional space of dimension `> 1`, one may find another
-vector linearly independent of the first one. -/
-theorem exists_linearIndependent_pair_of_one_lt_finrank
-    (h : 1 < finrank K V) {x : V} (hx : x ≠ 0) :
-    ∃ y, LinearIndependent K ![x, y] :=
-  exists_linearIndependent_pair_of_one_lt_rank (one_lt_rank_of_one_lt_finrank h) hx
-
-end Span
-
 section Basis
 
 open FiniteDimensional

Added a class HasRankNullity consisting of the rings that satisfy the rank-nullity theorem. Generalized the corollaries of the rank-nullity theorem from division rings to rings satisfying the class, and moved them into a new file LinearAlgebra.Dimension.RankNullity.

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

@@ -44,25 +44,35 @@ variable [Module R M] [Module R M'] [Module R M₁]
 
 section Quotient
 
+theorem LinearIndependent.sum_elim_of_quotient
+    {M' : Submodule R M} {ι₁ ι₂} {f : ι₁ → M'} (hf : LinearIndependent R f) (g : ι₂ → M)
+    (hg : LinearIndependent R (Submodule.Quotient.mk (p := M') ∘ g)) :
+      LinearIndependent R (Sum.elim (f · : ι₁ → M) g) := by
+  refine .sum_type (hf.map' M'.subtype M'.ker_subtype) (.of_comp M'.mkQ hg) ?_
+  refine disjoint_def.mpr fun x h₁ h₂ ↦ ?_
+  have : x ∈ M' := span_le.mpr (Set.range_subset_iff.mpr fun i ↦ (f i).prop) h₁
+  obtain ⟨c, rfl⟩ := Finsupp.mem_span_range_iff_exists_finsupp.mp h₂
+  simp_rw [← Quotient.mk_eq_zero, ← mkQ_apply, map_finsupp_sum, map_smul, mkQ_apply] at this
+  rw [linearIndependent_iff.mp hg _ this, Finsupp.sum_zero_index]
+
+theorem LinearIndependent.union_of_quotient
+    {M' : Submodule R M} {s : Set M} (hs : s ⊆ M') (hs' : LinearIndependent (ι := s) R Subtype.val)
+  {t : Set M} (ht : LinearIndependent (ι := t) R (Submodule.Quotient.mk (p := M') ∘ Subtype.val)) :
+    LinearIndependent (ι := (s ∪ t : _)) R Subtype.val := by
+  refine (LinearIndependent.sum_elim_of_quotient (f := Set.embeddingOfSubset s M' hs)
+    (of_comp M'.subtype (by simpa using hs')) Subtype.val ht).to_subtype_range' ?_
+  simp only [embeddingOfSubset_apply_coe, Sum.elim_range, Subtype.range_val]
+
 theorem rank_quotient_add_rank_le [Nontrivial R] (M' : Submodule R M) :
     Module.rank R (M ⧸ M') + Module.rank R M' ≤ Module.rank R M := by
-  simp_rw [Module.rank_def]
+  conv_lhs => simp only [Module.rank_def]
   have := nonempty_linearIndependent_set R (M ⧸ M')
   have := nonempty_linearIndependent_set R M'
   rw [Cardinal.ciSup_add_ciSup _ (bddAbove_range.{v, v} _) _ (bddAbove_range.{v, v} _)]
   refine ciSup_le fun ⟨s, hs⟩ ↦ ciSup_le fun ⟨t, ht⟩ ↦ ?_
   choose f hf using Quotient.mk_surjective M'
-  let g : s ⊕ t → M := Sum.elim (f ·) (·)
-  suffices LinearIndependent R g by
-    refine le_trans ?_ (le_ciSup (bddAbove_range.{v, v} _) ⟨_, this.to_subtype_range⟩)
-    rw [mk_range_eq _ this.injective, mk_sum, lift_id, lift_id]
-  refine .sum_type (.of_comp M'.mkQ ?_) (ht.map' M'.subtype M'.ker_subtype) ?_
-  · convert hs; ext x; exact hf x
-  refine disjoint_def.mpr fun x h₁ h₂ ↦ ?_
-  have : x ∈ M' := span_le.mpr (Set.range_subset_iff.mpr fun i ↦ i.1.2) h₂
-  obtain ⟨c, rfl⟩ := Finsupp.mem_span_range_iff_exists_finsupp.mp h₁
-  simp_rw [← Quotient.mk_eq_zero, ← mkQ_apply, map_finsupp_sum, map_smul, mkQ_apply, hf] at this
-  rw [linearIndependent_iff.mp hs _ this, Finsupp.sum_zero_index]
+  simpa [add_comm] using (LinearIndependent.sum_elim_of_quotient ht (fun (i : s) ↦ f i)
+    (by simpa [Function.comp, hf] using hs)).cardinal_le_rank
 
 theorem rank_quotient_le (p : Submodule R M) : Module.rank R (M ⧸ p) ≤ Module.rank R M :=
   (mkQ p).rank_le_of_surjective (surjective_quot_mk _)

I removed some redundant instance arguments throughout Mathlib. To do this, I used VS Code's regex search. See https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/repeating.20instances.20from.20variable.20command I closed the previous PR for this and reopened it.

@@ -67,7 +67,7 @@ lemma rank_eq_zero_iff :
 variable [Nontrivial R]
 variable [NoZeroSMulDivisors R M]
 
-theorem rank_zero_iff_forall_zero [NoZeroSMulDivisors R M] :
+theorem rank_zero_iff_forall_zero :
     Module.rank R M = 0 ↔ ∀ x : M, x = 0 := by
   simp_rw [rank_eq_zero_iff, smul_eq_zero, and_or_left, not_and_self_iff, false_or,
     exists_and_right, and_iff_right (exists_ne (0 : R))]
@@ -93,7 +93,7 @@ lemma rank_eq_zero_iff_isTorsion {R M} [CommRing R] [IsDomain R] [AddCommGroup M
   rw [Module.IsTorsion, rank_eq_zero_iff]
   simp [mem_nonZeroDivisors_iff_ne_zero]
 
-theorem rank_pos [NoZeroSMulDivisors R M] [Nontrivial M] : 0 < Module.rank R M :=
+theorem rank_pos [Nontrivial M] : 0 < Module.rank R M :=
   rank_pos_iff_nontrivial.mpr ‹_›
 #align rank_pos rank_pos
 
@@ -382,7 +382,7 @@ theorem FiniteDimensional.finrank_pos [NoZeroSMulDivisors R M] [h : Nontrivial M
 
 /-- See `FiniteDimensional.finrank_zero_iff`
   for the stronger version with `NoZeroSMulDivisors R M`. -/
-theorem FiniteDimensional.finrank_eq_zero_iff [Module.Finite R M] :
+theorem FiniteDimensional.finrank_eq_zero_iff :
     finrank R M = 0 ↔ ∀ x : M, ∃ a : R, a ≠ 0 ∧ a • x = 0 := by
   rw [← rank_eq_zero_iff (R := R), ← finrank_eq_rank]
   norm_cast

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)

@@ -43,7 +43,6 @@ noncomputable section
 universe u v w w'
 
 variable {R : Type u} {M : Type v} [Ring R] [AddCommGroup M] [Module R M]
-
 variable {ι : Type w} {ι' : Type w'}
 
 open BigOperators Cardinal Basis Submodule Function Set

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)

@@ -30,11 +30,8 @@ open BigOperators Cardinal Basis Submodule Function Set DirectSum FiniteDimensio
 section Tower
 
 variable (F : Type u) (K : Type v) (A : Type w)
-
 variable [Ring F] [Ring K] [AddCommGroup A]
-
 variable [Module F K] [Module K A] [Module F A] [IsScalarTower F K A]
-
 variable [StrongRankCondition F] [StrongRankCondition K] [Module.Free F K] [Module.Free K A]
 
 /-- Tower law: if `A` is a `K`-module and `K` is an extension of `F` then
@@ -73,13 +70,9 @@ theorem FiniteDimensional.finrank_mul_finrank : finrank F K * finrank K A = finr
 end Tower
 
 variable {R : Type u} {M M₁ : Type v} {M' : Type v'}
-
 variable [Ring R] [StrongRankCondition R]
-
 variable [AddCommGroup M] [Module R M] [Module.Free R M]
-
 variable [AddCommGroup M'] [Module R M'] [Module.Free R M']
-
 variable [AddCommGroup M₁] [Module R M₁] [Module.Free R M₁]
 
 namespace Module.Free

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)

@@ -24,9 +24,7 @@ noncomputable section
 universe u v v' w
 
 variable {R : Type u} {M M₁ : Type v} {M' : Type v'} {ι : Type w}
-
 variable [Ring R] [AddCommGroup M] [AddCommGroup M'] [AddCommGroup M₁]
-
 variable [Module R M] [Module R M'] [Module R M₁]
 
 attribute [local instance] nontrivial_of_invariantBasisNumber
@@ -67,7 +65,6 @@ lemma rank_eq_zero_iff :
     simpa using DFunLike.congr_fun (linearIndependent_iff.mp hs (Finsupp.single i a) (by simpa)) i
 
 variable [Nontrivial R]
-
 variable [NoZeroSMulDivisors R M]
 
 theorem rank_zero_iff_forall_zero [NoZeroSMulDivisors R M] :

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)

@@ -36,7 +36,6 @@ noncomputable section
 universe u v v' v'' u₁' w w'
 
 variable {K R : Type u} {V V₁ V₂ V₃ : Type v} {V' V'₁ : Type v'} {V'' : Type v''}
-
 variable {ι : Type w} {ι' : Type w'} {η : Type u₁'} {φ : η → Type*}
 
 open BigOperators Cardinal Basis Submodule Function Set
@@ -46,11 +45,8 @@ section Module
 section DivisionRing
 
 variable [DivisionRing K]
-
 variable [AddCommGroup V] [Module K V]
-
 variable [AddCommGroup V'] [Module K V']
-
 variable [AddCommGroup V₁] [Module K V₁]
 
 /-- If a vector space has a finite dimension, the index set of `Basis.ofVectorSpace` is finite. -/
@@ -117,7 +113,6 @@ theorem exists_linearIndependent_pair_of_one_lt_rank
 section
 
 variable [AddCommGroup V₂] [Module K V₂]
-
 variable [AddCommGroup V₃] [Module K V₃]
 
 open LinearMap
@@ -181,7 +176,6 @@ end
 end DivisionRing
 
 variable [DivisionRing K] [AddCommGroup V] [Module K V] [AddCommGroup V₁] [Module K V₁]
-
 variable [AddCommGroup V'] [Module K V']
 
 /-- The `ι` indexed basis on `V`, where `ι` is an empty type and `V` is zero-dimensional.
@@ -461,7 +455,6 @@ end Basis
 section Cardinal
 
 variable (K)
-
 variable [DivisionRing K]
 
 /-- Key lemma towards the Erdős-Kaplansky theorem from https://mathoverflow.net/a/168624 -/

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)

@@ -35,13 +35,11 @@ noncomputable section
 universe u v v' u₁' w w'
 
 variable {R S : Type u} {M : Type v} {M' : Type v'} {M₁ : Type v}
-
 variable {ι : Type w} {ι' : Type w'} {η : Type u₁'} {φ : η → Type*}
 
 open BigOperators Cardinal Basis Submodule Function Set FiniteDimensional DirectSum
 
 variable [Ring R] [CommRing S] [AddCommGroup M] [AddCommGroup M'] [AddCommGroup M₁]
-
 variable [Module R M] [Module R M'] [Module R M₁]
 
 section Quotient
@@ -118,7 +116,6 @@ theorem rank_add_rank_le_rank_prod [Nontrivial R] :
   convert ← lift_rank_add_lift_rank_le_rank_prod R M M₁ <;> apply lift_id
 
 variable {R M M'}
-
 variable [StrongRankCondition R] [Module.Free R M] [Module.Free R M'] [Module.Free R M₁]
 
 open Module.Free
@@ -149,7 +146,6 @@ end Prod
 section Finsupp
 
 variable (R M M')
-
 variable [StrongRankCondition R] [Module.Free R M] [Module.Free R M']
 
 open Module.Free BigOperators
@@ -253,7 +249,6 @@ end Finsupp
 section Pi
 
 variable [StrongRankCondition R] [Module.Free R M]
-
 variable [∀ i, AddCommGroup (φ i)] [∀ i, Module R (φ i)] [∀ i, Module.Free R (φ i)]
 
 open Module.Free
@@ -344,7 +339,6 @@ section TensorProduct
 open TensorProduct
 
 variable [StrongRankCondition S]
-
 variable [Module S M] [Module.Free S M] [Module S M'] [Module.Free S M']
 variable [Module S M₁] [Module.Free S M₁]
 

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)

@@ -44,7 +44,6 @@ section Module
 section
 
 variable [Semiring R] [AddCommMonoid M] [Module R M]
-
 variable (R M)
 
 /-- The rank of a module, defined as a term of type `Cardinal`.

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

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

@@ -309,11 +309,11 @@ theorem Module.exists_nontrivial_relation_sum_zero_of_finrank_succ_lt_card
   -- After this, it's a matter of verifying the properties,
   -- based on the corresponding properties for `g`.
   · rw [sum_map, Embedding.coeFn_mk] at gsum
-    simp_rw [← t.sum_erase_add _ x₀_mem, if_pos, neg_smul, sum_smul,
+    simp_rw [f, ← t.sum_erase_add _ x₀_mem, if_pos, neg_smul, sum_smul,
              ← sub_eq_add_neg, ← sum_sub_distrib, ← gsum, smul_sub]
     refine sum_congr rfl fun x x_mem ↦ ?_
     rw [if_neg (mem_erase.mp x_mem).1]
-  · simp_rw [← t.sum_erase_add _ x₀_mem, if_pos, add_neg_eq_zero]
+  · simp_rw [f, ← t.sum_erase_add _ x₀_mem, if_pos, add_neg_eq_zero]
     exact sum_congr rfl fun x x_mem ↦ if_neg (mem_erase.mp x_mem).1
   · obtain ⟨x₁, x₁_mem', rfl⟩ := Finset.mem_map.mp x₁_mem
     have := mem_erase.mp x₁_mem'

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -455,7 +455,7 @@ theorem FiniteDimensional.finrank_self : finrank R R = 1 :=
 noncomputable def Basis.unique {ι : Type*} (b : Basis ι R R) : Unique ι := by
   have A : Cardinal.mk ι = ↑(FiniteDimensional.finrank R R) :=
     (Module.mk_finrank_eq_card_basis b).symm
-  -- porting note: replace `algebraMap.coe_one` with `Nat.cast_one`
+  -- Porting note: replace `algebraMap.coe_one` with `Nat.cast_one`
   simp only [Cardinal.eq_one_iff_unique, FiniteDimensional.finrank_self, Nat.cast_one] at A
   exact Nonempty.some ((unique_iff_subsingleton_and_nonempty _).2 A)
 #align basis.unique Basis.unique
@@ -465,7 +465,7 @@ variable (M)
 /-- The rank of a finite module is finite. -/
 theorem rank_lt_aleph0 [Module.Finite R M] : Module.rank R M < ℵ₀ := by
   simp only [Module.rank_def]
-  -- porting note: can't use `‹_›` as that pulls the unused `N` into the context
+  -- Porting note: can't use `‹_›` as that pulls the unused `N` into the context
   obtain ⟨S, hS⟩ := Module.finite_def.mp ‹Module.Finite R M›
   refine' (ciSup_le' fun i => _).trans_lt (nat_lt_aleph0 S.card)
   exact linearIndependent_le_span_finset _ i.prop S hS

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to

• "simp can prove this"
• "simp can simplify this`"
• "was @[simp], now can be proved by simp"
• "was @[simp], but simp can prove it"
• "removed simp attribute as the equality can already be obtained by simp"
• "simp can already prove this"
• "simp already proves this"
• "simp can prove these"

@@ -319,7 +319,7 @@ theorem FiniteDimensional.finrank_fintype_fun_eq_card : finrank R (η → R) = F
 #align finite_dimensional.finrank_fintype_fun_eq_card FiniteDimensional.finrank_fintype_fun_eq_card
 
 /-- The vector space of functions on `Fin n` has finrank equal to `n`. -/
--- @[simp] -- Porting note: simp already proves this
+-- @[simp] -- Porting note (#10618): simp already proves this
 theorem FiniteDimensional.finrank_fin_fun {n : ℕ} : finrank R (Fin n → R) = n := by simp
 #align finite_dimensional.finrank_fin_fun FiniteDimensional.finrank_fin_fun
 

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

@@ -317,7 +317,8 @@ theorem Module.exists_nontrivial_relation_sum_zero_of_finrank_succ_lt_card
     exact sum_congr rfl fun x x_mem ↦ if_neg (mem_erase.mp x_mem).1
   · obtain ⟨x₁, x₁_mem', rfl⟩ := Finset.mem_map.mp x₁_mem
     have := mem_erase.mp x₁_mem'
-    exact ⟨x₁, by simpa only [Embedding.coeFn_mk, sub_add_cancel, this.2, true_and, if_neg this.1]⟩
+    exact ⟨x₁, by
+      simpa only [f, Embedding.coeFn_mk, sub_add_cancel, this.2, true_and, if_neg this.1]⟩
 #align finite_dimensional.exists_nontrivial_relation_sum_zero_of_rank_succ_lt_card Module.exists_nontrivial_relation_sum_zero_of_finrank_succ_lt_card
 
 end

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

@@ -230,11 +230,11 @@ theorem rank_le_one_iff : Module.rank K V ≤ 1 ↔ ∃ v₀ : V, ∀ v, ∃ r :
     rw [← b.mk_eq_rank'', Cardinal.le_one_iff_subsingleton, subsingleton_coe] at hd
     rcases eq_empty_or_nonempty (ofVectorSpaceIndex K V) with (hb | ⟨⟨v₀, hv₀⟩⟩)
     · use 0
-      have h' : ∀ v : V, v = 0 := by simpa [hb, Submodule.eq_bot_iff] using b.span_eq.symm
+      have h' : ∀ v : V, v = 0 := by simpa [b, hb, Submodule.eq_bot_iff] using b.span_eq.symm
       intro v
       simp [h' v]
     · use v₀
-      have h' : (K ∙ v₀) = ⊤ := by simpa [hd.eq_singleton_of_mem hv₀] using b.span_eq
+      have h' : (K ∙ v₀) = ⊤ := by simpa [b, hd.eq_singleton_of_mem hv₀] using b.span_eq
       intro v
       have hv : v ∈ (⊤ : Submodule K V) := mem_top
       rwa [← h', mem_span_singleton] at hv
@@ -410,13 +410,13 @@ theorem linearIndependent_iff_card_eq_finrank_span {ι : Type*} [Fintype ι] {b
       have h : span K (f '' Set.range b') = map f (span K (Set.range b')) := span_image f
       have hf : f '' Set.range b' = Set.range b := by
         ext x
-        simp [Set.mem_image, Set.mem_range]
+        simp [f, Set.mem_image, Set.mem_range]
       rw [hf] at h
       have hx : (x : V) ∈ span K (Set.range b) := x.property
       conv at hx =>
         arg 2
         rw [h]
-      simpa [mem_map] using hx
+      simpa [f, mem_map] using hx
     have hi : LinearMap.ker f = ⊥ := ker_subtype _
     convert (linearIndependent_of_top_le_span_of_card_eq_finrank hs hc).map' _ hi
 #align linear_independent_iff_card_eq_finrank_span linearIndependent_iff_card_eq_finrank_span

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

@@ -209,7 +209,7 @@ theorem rank_matrix' (m n : Type v) [Finite m] [Finite n] :
 
 /-- If `m` and `n` are `Fintype` that lie in the same universe as `R`, the rank of `m × n` matrices
   is `# m * # n`. -/
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem rank_matrix'' (m n : Type u) [Finite m] [Finite n] :
     Module.rank R (Matrix m n R) = #m * #n := by simp
 #align rank_matrix'' rank_matrix''

Remove unnecessary "rw"s.

@@ -304,7 +304,7 @@ theorem rank_fun_eq_lift_mul : Module.rank R (η → M) =
 #align rank_fun_eq_lift_mul rank_fun_eq_lift_mul
 
 theorem rank_fun' : Module.rank R (η → R) = Fintype.card η := by
-  rw [rank_fun_eq_lift_mul, rank_self, Cardinal.lift_one, mul_one, Cardinal.natCast_inj]
+  rw [rank_fun_eq_lift_mul, rank_self, Cardinal.lift_one, mul_one]
 #align rank_fun' rank_fun'
 
 theorem rank_fin_fun (n : ℕ) : Module.rank R (Fin n → R) = n := by simp [rank_fun']

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>

@@ -52,8 +52,8 @@ lemma rank_eq_zero_iff :
   · contrapose!
     rintro ⟨x, hx⟩
     rw [← Cardinal.one_le_iff_ne_zero]
-    have : LinearIndependent R (fun _ : Unit ↦ x)
-    · exact linearIndependent_iff.mpr (fun l hl ↦ Finsupp.unique_ext <| not_not.mp fun H ↦
+    have : LinearIndependent R (fun _ : Unit ↦ x) :=
+      linearIndependent_iff.mpr (fun l hl ↦ Finsupp.unique_ext <| not_not.mp fun H ↦
         hx _ H ((Finsupp.total_unique _ _ _).symm.trans hl))
     simpa using this.cardinal_lift_le_rank
   · intro h

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>

@@ -474,14 +474,14 @@ theorem max_aleph0_card_le_rank_fun_nat : max ℵ₀ #K ≤ Module.rank K (ℕ 
   by_contra!
   obtain ⟨⟨ιK, bK⟩⟩ := Module.Free.exists_basis (R := K) (M := ℕ → K)
   let L := Subfield.closure (Set.range (fun i : ιK × ℕ ↦ bK i.1 i.2))
-  have hLK : #L < #K
-  · refine (Subfield.cardinal_mk_closure_le_max _).trans_lt
+  have hLK : #L < #K := by
+    refine (Subfield.cardinal_mk_closure_le_max _).trans_lt
       (max_lt_iff.mpr ⟨mk_range_le.trans_lt ?_, card_K⟩)
     rwa [mk_prod, ← aleph0, lift_uzero, bK.mk_eq_rank'', mul_aleph0_eq aleph0_le]
   letI := Module.compHom K (RingHom.op L.subtype)
   obtain ⟨⟨ιL, bL⟩⟩ := Module.Free.exists_basis (R := Lᵐᵒᵖ) (M := K)
-  have card_ιL : ℵ₀ ≤ #ιL
-  · contrapose! hLK
+  have card_ιL : ℵ₀ ≤ #ιL := by
+    contrapose! hLK
     haveI := @Fintype.ofFinite _ (lt_aleph0_iff_finite.mp hLK)
     rw [bL.repr.toEquiv.cardinal_eq, mk_finsupp_of_fintype,
         ← MulOpposite.opEquiv.cardinal_eq] at card_K ⊢

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>

@@ -55,8 +55,8 @@ theorem rank_quotient_add_rank_le [Nontrivial R] (M' : Submodule R M) :
   refine ciSup_le fun ⟨s, hs⟩ ↦ ciSup_le fun ⟨t, ht⟩ ↦ ?_
   choose f hf using Quotient.mk_surjective M'
   let g : s ⊕ t → M := Sum.elim (f ·) (·)
-  suffices : LinearIndependent R g
-  · refine le_trans ?_ (le_ciSup (bddAbove_range.{v, v} _) ⟨_, this.to_subtype_range⟩)
+  suffices LinearIndependent R g by
+    refine le_trans ?_ (le_ciSup (bddAbove_range.{v, v} _) ⟨_, this.to_subtype_range⟩)
     rw [mk_range_eq _ this.injective, mk_sum, lift_id, lift_id]
   refine .sum_type (.of_comp M'.mkQ ?_) (ht.map' M'.subtype M'.ker_subtype) ?_
   · convert hs; ext x; exact hf x

Redefine these operations in terms of toENat.

@@ -193,8 +193,9 @@ lemma Module.rank_lt_alpeh0_iff :
 
 theorem FiniteDimensional.finrank_of_not_finite
     (h : ¬Module.Finite R M) :
-    finrank R M = 0 :=
-  dif_neg (Module.rank_lt_alpeh0_iff.not.mpr h)
+    finrank R M = 0 := by
+  rw [finrank, toNat_eq_zero, ← not_lt, Module.rank_lt_alpeh0_iff]
+  exact .inr h
 
 theorem Module.finite_of_finrank_pos (h : 0 < finrank R M) :
     Module.Finite R M := by

Redefine these operations in terms of toENat.

@@ -399,17 +399,15 @@ variable [StrongRankCondition R]
 
 /-- The dimension of a submodule is bounded by the dimension of the ambient space. -/
 theorem Submodule.finrank_le [Module.Finite R M] (s : Submodule R M) :
-    finrank R s ≤ finrank R M := by
-  simpa only [Cardinal.toNat_lift] using
-    toNat_le_of_le_of_lt_aleph0 (rank_lt_aleph0 _ _) (rank_submodule_le s)
+    finrank R s ≤ finrank R M :=
+  toNat_le_toNat (rank_submodule_le s) (rank_lt_aleph0 _ _)
 #align submodule.finrank_le Submodule.finrank_le
 
 /-- The dimension of a quotient is bounded by the dimension of the ambient space. -/
 theorem Submodule.finrank_quotient_le [Module.Finite R M] (s : Submodule R M) :
-    finrank R (M ⧸ s) ≤ finrank R M := by
-  simpa only [Cardinal.toNat_lift] using
-    toNat_le_of_le_of_lt_aleph0 (rank_lt_aleph0 _ _)
-      ((Submodule.mkQ s).rank_le_of_surjective (surjective_quot_mk _))
+    finrank R (M ⧸ s) ≤ finrank R M :=
+  toNat_le_toNat ((Submodule.mkQ s).rank_le_of_surjective (surjective_quot_mk _))
+    (rank_lt_aleph0 _ _)
 #align submodule.finrank_quotient_le Submodule.finrank_quotient_le
 
 /-- Pushforwards of finite submodules have a smaller finrank. -/

Fix minor typos in the following files:

• Mathlib/GroupTheory/GroupAction/Opposite.lean
• Mathlib/Init/Control/Lawful.lean
• Mathlib/ModelTheory/ElementarySubstructures.lean
• Mathlib/Algebra/Group/Defs.lean
• Mathlib/Algebra/Group/WithOne/Basic.lean
• Mathlib/Data/Int/Cast/Defs.lean
• Mathlib/LinearAlgebra/Dimension/Basic.lean
• Mathlib/NumberTheory/NumberField/CanonicalEmbedding.lean
• Mathlib/Algebra/Star/StarAlgHom.lean
• Mathlib/AlgebraicTopology/SimplexCategory.lean
• Mathlib/CategoryTheory/Abelian/Homology.lean
• Mathlib/CategoryTheory/Sites/Grothendieck.lean
• Mathlib/RingTheory/IsTensorProduct.lean
• Mathlib/AlgebraicTopology/DoldKan/Homotopies.lean
• Mathlib/AlgebraicTopology/ExtraDegeneracy.lean
• Mathlib/AlgebraicTopology/Nerve.lean
• Mathlib/AlgebraicTopology/SplitSimplicialObject.lean
• Mathlib/Analysis/ConstantSpeed.lean
• Mathlib/Analysis/Convolution.lean

@@ -179,7 +179,7 @@ variable {R : Type w} {S : Type v} [CommRing R] [Ring S] [Algebra R S]
   {R' : Type w'} {S' : Type v'} [CommRing R'] [Ring S'] [Algebra R' S']
 
 /-- If `S / R` and `S' / R'` are algebras, `i : R' →+* R` and `j : S →+* S'` are injective ring
-homorphisms, such that `R' → R → S → S'` and `R' → S'` commute, then the rank of `S / R` is
+homomorphisms, such that `R' → R → S → S'` and `R' → S'` commute, then the rank of `S / R` is
 smaller than or equal to the rank of `S' / R'`. -/
 theorem lift_rank_le_of_injective_injective
     (i : R' →+* R) (j : S →+* S') (hi : Injective i) (hj : Injective j)
@@ -192,7 +192,7 @@ theorem lift_rank_le_of_injective_injective
   simp_rw [smul_def, AddMonoidHom.coe_coe, map_mul, this]
 
 /-- If `S / R` and `S' / R'` are algebras, `i : R →+* R'` is a surjective ring homomorphism,
-`j : S →+* S'` is an injective ring homorphism, such that `R → R' → S'` and `R → S → S'` commute,
+`j : S →+* S'` is an injective ring homomorphism, such that `R → R' → S'` and `R → S → S'` commute,
 then the rank of `S / R` is smaller than or equal to the rank of `S' / R'`. -/
 theorem lift_rank_le_of_surjective_injective
     (i : R →+* R') (j : S →+* S') (hi : Surjective i) (hj : Injective j)

@@ -190,9 +190,9 @@ theorem lt_aleph0_of_finite {ι : Type w}
     [Module.Finite R M] {v : ι → M} (h : LinearIndependent R v) : #ι < ℵ₀ := by
   apply Cardinal.lift_lt.1
   apply lt_of_le_of_lt
-  apply h.cardinal_lift_le_rank
-  rw [← finrank_eq_rank, Cardinal.lift_aleph0, Cardinal.lift_natCast]
-  apply Cardinal.nat_lt_aleph0
+  · apply h.cardinal_lift_le_rank
+  · rw [← finrank_eq_rank, Cardinal.lift_aleph0, Cardinal.lift_natCast]
+    apply Cardinal.nat_lt_aleph0
 
 theorem finite [Module.Finite R M] {ι : Type*} {f : ι → M}
     (h : LinearIndependent R f) : Finite ι :=
@@ -364,20 +364,16 @@ variable [StrongRankCondition R] [Module.Finite R M]
 
 /-- A finite rank torsion-free module has positive `finrank` iff it has a nonzero element. -/
 theorem FiniteDimensional.finrank_pos_iff_exists_ne_zero [NoZeroSMulDivisors R M] :
-    0 < finrank R M ↔ ∃ x : M, x ≠ 0 :=
-  Iff.trans
-    (by
-      rw [← finrank_eq_rank]
-      norm_cast)
-    (@rank_pos_iff_exists_ne_zero R M _ _ _ _ _)
+    0 < finrank R M ↔ ∃ x : M, x ≠ 0 := by
+  rw [← @rank_pos_iff_exists_ne_zero R M, ← finrank_eq_rank]
+  norm_cast
 #align finite_dimensional.finrank_pos_iff_exists_ne_zero FiniteDimensional.finrank_pos_iff_exists_ne_zero
 
 /-- An `R`-finite torsion-free module has positive `finrank` iff it is nontrivial. -/
 theorem FiniteDimensional.finrank_pos_iff [NoZeroSMulDivisors R M] :
-    0 < finrank R M ↔ Nontrivial M :=
-  Iff.trans
-    (by rw [← finrank_eq_rank]; norm_cast)
-    (rank_pos_iff_nontrivial (R := R))
+    0 < finrank R M ↔ Nontrivial M := by
+  rw [← rank_pos_iff_nontrivial (R := R), ← finrank_eq_rank]
+  norm_cast
 #align finite_dimensional.finrank_pos_iff FiniteDimensional.finrank_pos_iff
 
 /-- A nontrivial finite dimensional space has positive `finrank`. -/
@@ -389,26 +385,23 @@ theorem FiniteDimensional.finrank_pos [NoZeroSMulDivisors R M] [h : Nontrivial M
 /-- See `FiniteDimensional.finrank_zero_iff`
   for the stronger version with `NoZeroSMulDivisors R M`. -/
 theorem FiniteDimensional.finrank_eq_zero_iff [Module.Finite R M] :
-    finrank R M = 0 ↔ ∀ x : M, ∃ a : R, a ≠ 0 ∧ a • x = 0 :=
-  Iff.trans
-    (by rw [← finrank_eq_rank]; norm_cast)
-    (rank_eq_zero_iff (R := R))
+    finrank R M = 0 ↔ ∀ x : M, ∃ a : R, a ≠ 0 ∧ a • x = 0 := by
+  rw [← rank_eq_zero_iff (R := R), ← finrank_eq_rank]
+  norm_cast
 
 /-- The `StrongRankCondition` is automatic. See `commRing_strongRankCondition`. -/
 theorem FiniteDimensional.finrank_eq_zero_iff_isTorsion {R} [CommRing R] [StrongRankCondition R]
     [IsDomain R] [Module R M] [Module.Finite R M] :
-    finrank R M = 0 ↔ Module.IsTorsion R M :=
-  Iff.trans
-    (by rw [← finrank_eq_rank]; norm_cast)
-    (rank_eq_zero_iff_isTorsion (R := R))
+    finrank R M = 0 ↔ Module.IsTorsion R M := by
+  rw [← rank_eq_zero_iff_isTorsion (R := R), ← finrank_eq_rank]
+  norm_cast
 
 /-- A finite dimensional space has zero `finrank` iff it is a subsingleton.
 This is the `finrank` version of `rank_zero_iff`. -/
 theorem FiniteDimensional.finrank_zero_iff [NoZeroSMulDivisors R M] :
-    finrank R M = 0 ↔ Subsingleton M :=
-  Iff.trans
-    (by rw [← finrank_eq_rank]; norm_cast)
-    (rank_zero_iff (R := R))
+    finrank R M = 0 ↔ Subsingleton M := by
+  rw [← rank_zero_iff (R := R), ← finrank_eq_rank]
+  norm_cast
 #align finite_dimensional.finrank_zero_iff FiniteDimensional.finrank_zero_iff
 
 end StrongRankCondition

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

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

@@ -3,10 +3,10 @@ Copyright (c) 2018 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 -/
-import Mathlib.LinearAlgebra.Dimension.Free
 import Mathlib.Algebra.Module.Torsion
 import Mathlib.SetTheory.Cardinal.Cofinality
 import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
+import Mathlib.LinearAlgebra.Dimension.StrongRankCondition
 
 
 #align_import linear_algebra.dimension from "leanprover-community/mathlib"@"47a5f8186becdbc826190ced4312f8199f9db6a5"

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

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

@@ -3,7 +3,7 @@ Copyright (c) 2018 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison, Chris Hughes, Anne Baanen
 -/
-import Mathlib.LinearAlgebra.Dimension.Finite
+import Mathlib.LinearAlgebra.Dimension.Free
 import Mathlib.Algebra.Module.Torsion
 
 #align_import linear_algebra.dimension from "leanprover-community/mathlib"@"47a5f8186becdbc826190ced4312f8199f9db6a5"

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

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

@@ -3,9 +3,7 @@ Copyright (c) 2018 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 -/
-import Mathlib.LinearAlgebra.DFinsupp
-import Mathlib.LinearAlgebra.Quotient
-import Mathlib.SetTheory.Cardinal.Ordinal
+import Mathlib.LinearAlgebra.LinearIndependent
 
 #align_import linear_algebra.dimension from "leanprover-community/mathlib"@"47a5f8186becdbc826190ced4312f8199f9db6a5"
 

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>

@@ -64,7 +64,7 @@ lemma rank_eq_zero_iff :
     rintro ⟨i : s⟩
     obtain ⟨a, ha, ha'⟩ := h i
     apply ha
-    simpa using FunLike.congr_fun (linearIndependent_iff.mp hs (Finsupp.single i a) (by simpa)) i
+    simpa using DFunLike.congr_fun (linearIndependent_iff.mp hs (Finsupp.single i a) (by simpa)) i
 
 variable [Nontrivial R]
 

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>

@@ -467,7 +467,7 @@ variable [DivisionRing K]
 /-- Key lemma towards the Erdős-Kaplansky theorem from https://mathoverflow.net/a/168624 -/
 theorem max_aleph0_card_le_rank_fun_nat : max ℵ₀ #K ≤ Module.rank K (ℕ → K) := by
   have aleph0_le : ℵ₀ ≤ Module.rank K (ℕ → K) := (rank_finsupp_self K ℕ).symm.trans_le
-    (Finsupp.lcoeFun.rank_le_of_injective <| by exact FunLike.coe_injective)
+    (Finsupp.lcoeFun.rank_le_of_injective <| by exact DFunLike.coe_injective)
   refine max_le aleph0_le ?_
   obtain card_K | card_K := le_or_lt #K ℵ₀
   · exact card_K.trans aleph0_le

Generalize the conditions of the tower law FiniteDimensional.finrank_mul_finrank' in FieldTheory/Tower from [CommRing F] [Algebra F K] to [Ring F] [Module F K], and remove the [Module.Finite F K] and [Module.Finite K A] conditions.

The generalized version applies to situations when we have a tower C/B/A where the A-module structure on C is induced from the B-module structure via a RingHom from A to B, and the A-module structure on B is induced by the same RingHom. In particular, it applies when the A-module structure on B and the B-module structure on C come from two RingHoms, and the A-module structure on C comes from the composition of them, regardless of whether A and B are commutative or not.

As prerequisites, I also generalized lemmas originally introduced by @kckennylau in [mathlib3#3355](https://github.com/leanprover-community/mathlib/pull/3355/files) to prove the tower law. They were split into three PRs:

• LinearAlgebra/Span #9380: 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.

• Algebra/Tower #9382: switching from CommSemiring/Algebra to Semiring/Module here requires proving the curious lemma IsScalarTower.isLinearMap which states that for a tower of modules A/S/R, any S-linear map from S to A is also R-linear. If the map is injective, we can deduce that S/S/R also form a tower. (By ringHomEquivModuleIsScalarTower in #9381, there is therefore a canonical RingHom from R to S.)

• Lemmas for free modules over rings including finrank_mul_finrank' are moved from FieldTheory/Tower to LinearAlgebra/Dimension/Free

Zulip

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

@@ -23,12 +23,57 @@ import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
 
 noncomputable section
 
-universe u v v'
-
-variable {R : Type u} {M M₁ : Type v} {M' : Type v'}
+universe u v v' w
 
 open BigOperators Cardinal Basis Submodule Function Set DirectSum FiniteDimensional
 
+section Tower
+
+variable (F : Type u) (K : Type v) (A : Type w)
+
+variable [Ring F] [Ring K] [AddCommGroup A]
+
+variable [Module F K] [Module K A] [Module F A] [IsScalarTower F K A]
+
+variable [StrongRankCondition F] [StrongRankCondition K] [Module.Free F K] [Module.Free K A]
+
+/-- Tower law: if `A` is a `K`-module and `K` is an extension of `F` then
+$\operatorname{rank}_F(A) = \operatorname{rank}_F(K) * \operatorname{rank}_K(A)$.
+
+The universe polymorphic version of `rank_mul_rank` below. -/
+theorem lift_rank_mul_lift_rank :
+    Cardinal.lift.{w} (Module.rank F K) * Cardinal.lift.{v} (Module.rank K A) =
+      Cardinal.lift.{v} (Module.rank F A) := by
+  let b := Module.Free.chooseBasis F K
+  let c := Module.Free.chooseBasis K A
+  rw [← (Module.rank F K).lift_id, ← b.mk_eq_rank, ← (Module.rank K A).lift_id, ← c.mk_eq_rank,
+    ← lift_umax.{w, v}, ← (b.smul c).mk_eq_rank, mk_prod, lift_mul, lift_lift, lift_lift, lift_lift,
+    lift_lift, lift_umax.{v, w}]
+#align lift_rank_mul_lift_rank lift_rank_mul_lift_rank
+
+/-- Tower law: if `A` is a `K`-module and `K` is an extension of `F` then
+$\operatorname{rank}_F(A) = \operatorname{rank}_F(K) * \operatorname{rank}_K(A)$.
+
+This is a simpler version of `lift_rank_mul_lift_rank` with `K` and `A` in the same universe. -/
+theorem rank_mul_rank (A : Type v) [AddCommGroup A]
+    [Module K A] [Module F A] [IsScalarTower F K A] [Module.Free K A] :
+    Module.rank F K * Module.rank K A = Module.rank F A := by
+  convert lift_rank_mul_lift_rank F K A <;> rw [lift_id]
+#align rank_mul_rank rank_mul_rank
+
+/-- Tower law: if `A` is a `K`-module and `K` is an extension of `F` then
+$\operatorname{rank}_F(A) = \operatorname{rank}_F(K) * \operatorname{rank}_K(A)$. -/
+theorem FiniteDimensional.finrank_mul_finrank : finrank F K * finrank K A = finrank F A := by
+  simp_rw [finrank]
+  rw [← toNat_lift.{w} (Module.rank F K), ← toNat_lift.{v} (Module.rank K A), ← toNat_mul,
+    lift_rank_mul_lift_rank, toNat_lift]
+#align finite_dimensional.finrank_mul_finrank FiniteDimensional.finrank_mul_finrank
+#align finite_dimensional.finrank_mul_finrank' FiniteDimensional.finrank_mul_finrank
+
+end Tower
+
+variable {R : Type u} {M M₁ : Type v} {M' : Type v'}
+
 variable [Ring R] [StrongRankCondition R]
 
 variable [AddCommGroup M] [Module R M] [Module.Free R M]

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

@@ -59,13 +59,6 @@ theorem Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0 (h : Module.rank K V <
   finite_def.2 <| (Basis.ofVectorSpace K V).nonempty_fintype_index_of_rank_lt_aleph0 h
 #align basis.finite_of_vector_space_index_of_rank_lt_aleph_0 Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0
 
--- TODO how far can we generalise this?
-theorem rank_span_le (s : Set V) : Module.rank K (span K s) ≤ #s := by
-  obtain ⟨b, hb, hsab, hlib⟩ := exists_linearIndependent K s
-  convert Cardinal.mk_le_mk_of_subset hb
-  rw [← hsab, rank_span_set hlib]
-#align rank_span_le rank_span_le
-
 theorem rank_quotient_add_rank (p : Submodule K V) :
     Module.rank K (V ⧸ p) + Module.rank K p = Module.rank K V := by
   classical
@@ -326,68 +319,6 @@ open Submodule FiniteDimensional
 
 variable [DivisionRing K] [AddCommGroup V] [Module K V]
 
-variable (K)
-
-/-- The rank of a set of vectors as a natural number. -/
-protected noncomputable def Set.finrank (s : Set V) : ℕ :=
-  finrank K (span K s)
-#align set.finrank Set.finrank
-
-variable {K}
-
-theorem finrank_span_le_card (s : Set V) [Fintype s] : finrank K (span K s) ≤ s.toFinset.card :=
-  finrank_le_of_rank_le (by simpa using rank_span_le (K := K) s)
-#align finrank_span_le_card finrank_span_le_card
-
-theorem finrank_span_finset_le_card (s : Finset V) : (s : Set V).finrank K ≤ s.card :=
-  calc
-    (s : Set V).finrank K ≤ (s : Set V).toFinset.card := finrank_span_le_card (V := V) s
-    _ = s.card := by simp
-#align finrank_span_finset_le_card finrank_span_finset_le_card
-
-theorem finrank_range_le_card {ι : Type*} [Fintype ι] {b : ι → V} :
-    (Set.range b).finrank K ≤ Fintype.card ι := by
-  classical
-  refine (finrank_span_le_card _).trans ?_
-  rw [Set.toFinset_range]
-  exact Finset.card_image_le
-#align finrank_range_le_card finrank_range_le_card
-
-theorem finrank_span_eq_card {ι : Type*} [Fintype ι] {b : ι → V} (hb : LinearIndependent K b) :
-    finrank K (span K (Set.range b)) = Fintype.card ι :=
-  finrank_eq_of_rank_eq
-    (by
-      have : Module.rank K (span K (Set.range b)) = #(Set.range b) := rank_span hb
-      rwa [← lift_inj, mk_range_eq_of_injective hb.injective, Cardinal.mk_fintype, lift_natCast,
-        lift_eq_nat_iff] at this)
-#align finrank_span_eq_card finrank_span_eq_card
-
-theorem finrank_span_set_eq_card (s : Set V) [Fintype s] (hs : LinearIndependent K ((↑) : s → V)) :
-    finrank K (span K s) = s.toFinset.card :=
-  finrank_eq_of_rank_eq
-    (by
-      have : Module.rank K (span K s) = #s := rank_span_set hs
-      rwa [Cardinal.mk_fintype, ← Set.toFinset_card] at this)
-#align finrank_span_set_eq_card finrank_span_set_eq_card
-
-theorem finrank_span_finset_eq_card (s : Finset V) (hs : LinearIndependent K ((↑) : s → V)) :
-    finrank K (span K (s : Set V)) = s.card := by
-  convert finrank_span_set_eq_card (s : Set V) hs
-  ext
-  simp
-#align finrank_span_finset_eq_card finrank_span_finset_eq_card
-
-theorem span_lt_of_subset_of_card_lt_finrank {s : Set V} [Fintype s] {t : Submodule K V}
-    (subset : s ⊆ t) (card_lt : s.toFinset.card < finrank K t) : span K s < t :=
-  lt_of_le_of_finrank_lt_finrank (span_le.mpr subset)
-    (lt_of_le_of_lt (finrank_span_le_card _) card_lt)
-#align span_lt_of_subset_of_card_lt_finrank span_lt_of_subset_of_card_lt_finrank
-
-theorem span_lt_top_of_card_lt_finrank {s : Set V} [Fintype s]
-    (card_lt : s.toFinset.card < finrank K V) : span K s < ⊤ :=
-  lt_top_of_finrank_lt_finrank (lt_of_le_of_lt (finrank_span_le_card _) card_lt)
-#align span_lt_top_of_card_lt_finrank span_lt_top_of_card_lt_finrank
-
 /-- Given a family of `n` linearly independent vectors in a finite-dimensional space of
 dimension `> n`, one may extend the family by another vector while retaining linear independence. -/
 theorem exists_linearIndependent_snoc_of_lt_finrank {n : ℕ} {v : Fin n → V}
@@ -492,7 +423,7 @@ theorem linearIndependent_iff_card_eq_finrank_span {ι : Type*} [Fintype ι] {b
 
 theorem linearIndependent_iff_card_le_finrank_span {ι : Type*} [Fintype ι] {b : ι → V} :
     LinearIndependent K b ↔ Fintype.card ι ≤ (Set.range b).finrank K := by
-  rw [linearIndependent_iff_card_eq_finrank_span, finrank_range_le_card.le_iff_eq]
+  rw [linearIndependent_iff_card_eq_finrank_span, (finrank_range_le_card _).le_iff_eq]
 #align linear_independent_iff_card_le_finrank_span linearIndependent_iff_card_le_finrank_span
 
 /-- A family of `finrank K V` vectors forms a basis if they span the whole space. -/

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

@@ -374,27 +374,6 @@ theorem FiniteDimensional.finrank_tensorProduct :
 
 end TensorProduct
 
-section Span
-
-variable [StrongRankCondition R]
-
-theorem rank_span_le_of_finite {s : Set M} (hs : s.Finite) : Module.rank R (span R s) ≤ #s := by
-  rw [Module.rank_def]
-  apply ciSup_le'
-  rintro ⟨t, ht⟩
-  letI := hs.fintype
-  simpa [Cardinal.mk_image_eq Subtype.val_injective] using linearIndependent_le_span' _
-    (ht.map (f := Submodule.subtype _) (by simp)).image s (fun x ↦ by aesop)
-
-theorem rank_span_finset_le (s : Finset M) : Module.rank R (span R (s : Set M)) ≤ s.card := by
-  simpa using rank_span_le_of_finite s.finite_toSet
-
-theorem rank_span_of_finset (s : Finset M) : Module.rank R (span R (s : Set M)) < ℵ₀ :=
-  (rank_span_finset_le s).trans_lt (Cardinal.nat_lt_aleph0 _)
-#align rank_span_of_finset rank_span_of_finset
-
-end Span
-
 section SubmoduleRank
 
 section
@@ -449,9 +428,93 @@ theorem Submodule.finrank_le_finrank_of_le {s t : Submodule R M} [Module.Finite
 
 end
 
-
 end SubmoduleRank
 
+section Span
+
+variable [StrongRankCondition R]
+
+theorem rank_span_le (s : Set M) : Module.rank R (span R s) ≤ #s := by
+  rw [Finsupp.span_eq_range_total, ← lift_strictMono.le_iff_le]
+  refine (lift_rank_range_le _).trans ?_
+  rw [rank_finsupp_self]
+  simp only [lift_lift, ge_iff_le, le_refl]
+#align rank_span_le rank_span_le
+
+theorem rank_span_finset_le (s : Finset M) : Module.rank R (span R (s : Set M)) ≤ s.card := by
+  simpa using rank_span_le s.toSet
+
+theorem rank_span_of_finset (s : Finset M) : Module.rank R (span R (s : Set M)) < ℵ₀ :=
+  (rank_span_finset_le s).trans_lt (Cardinal.nat_lt_aleph0 _)
+#align rank_span_of_finset rank_span_of_finset
+
+open Submodule FiniteDimensional
+
+variable (R)
+
+/-- The rank of a set of vectors as a natural number. -/
+protected noncomputable def Set.finrank (s : Set M) : ℕ :=
+  finrank R (span R s)
+#align set.finrank Set.finrank
+
+variable {R}
+
+theorem finrank_span_le_card (s : Set M) [Fintype s] : finrank R (span R s) ≤ s.toFinset.card :=
+  finrank_le_of_rank_le (by simpa using rank_span_le (R := R) s)
+#align finrank_span_le_card finrank_span_le_card
+
+theorem finrank_span_finset_le_card (s : Finset M) : (s : Set M).finrank R ≤ s.card :=
+  calc
+    (s : Set M).finrank R ≤ (s : Set M).toFinset.card := finrank_span_le_card (M := M) s
+    _ = s.card := by simp
+#align finrank_span_finset_le_card finrank_span_finset_le_card
+
+theorem finrank_range_le_card {ι : Type*} [Fintype ι] (b : ι → M) :
+    (Set.range b).finrank R ≤ Fintype.card ι := by
+  classical
+  refine (finrank_span_le_card _).trans ?_
+  rw [Set.toFinset_range]
+  exact Finset.card_image_le
+#align finrank_range_le_card finrank_range_le_card
+
+theorem finrank_span_eq_card [Nontrivial R] {ι : Type*} [Fintype ι] {b : ι → M}
+    (hb : LinearIndependent R b) :
+    finrank R (span R (Set.range b)) = Fintype.card ι :=
+  finrank_eq_of_rank_eq
+    (by
+      have : Module.rank R (span R (Set.range b)) = #(Set.range b) := rank_span hb
+      rwa [← lift_inj, mk_range_eq_of_injective hb.injective, Cardinal.mk_fintype, lift_natCast,
+        lift_eq_nat_iff] at this)
+#align finrank_span_eq_card finrank_span_eq_card
+
+theorem finrank_span_set_eq_card {s : Set M} [Fintype s] (hs : LinearIndependent R ((↑) : s → M)) :
+    finrank R (span R s) = s.toFinset.card :=
+  finrank_eq_of_rank_eq
+    (by
+      have : Module.rank R (span R s) = #s := rank_span_set hs
+      rwa [Cardinal.mk_fintype, ← Set.toFinset_card] at this)
+#align finrank_span_set_eq_card finrank_span_set_eq_card
+
+theorem finrank_span_finset_eq_card {s : Finset M} (hs : LinearIndependent R ((↑) : s → M)) :
+    finrank R (span R (s : Set M)) = s.card := by
+  convert finrank_span_set_eq_card (s := (s : Set M)) hs
+  ext
+  simp
+#align finrank_span_finset_eq_card finrank_span_finset_eq_card
+
+theorem span_lt_of_subset_of_card_lt_finrank {s : Set M} [Fintype s] {t : Submodule R M}
+    (subset : s ⊆ t) (card_lt : s.toFinset.card < finrank R t) : span R s < t :=
+  lt_of_le_of_finrank_lt_finrank (span_le.mpr subset)
+    (lt_of_le_of_lt (finrank_span_le_card _) card_lt)
+#align span_lt_of_subset_of_card_lt_finrank span_lt_of_subset_of_card_lt_finrank
+
+theorem span_lt_top_of_card_lt_finrank {s : Set M} [Fintype s]
+    (card_lt : s.toFinset.card < finrank R M) : span R s < ⊤ :=
+  lt_top_of_finrank_lt_finrank (lt_of_le_of_lt (finrank_span_le_card _) card_lt)
+#align span_lt_top_of_card_lt_finrank span_lt_top_of_card_lt_finrank
+
+end Span
+
 section SubalgebraRank
 
 open Module

• @[mk_iff] class MyPred now generates myPred_iff, not MyPred_iff
• add Lean.Name.decapitalize
• fix indentation and a few typos in the docs/comments.

Partially addresses issue #9129

@@ -302,7 +302,7 @@ theorem rank_submodule_le_one_iff' (s : Submodule K V) :
 
 theorem Submodule.rank_le_one_iff_isPrincipal (W : Submodule K V) :
     Module.rank K W ≤ 1 ↔ W.IsPrincipal := by
-  simp only [rank_le_one_iff, Submodule.IsPrincipal_iff, le_antisymm_iff, le_span_singleton_iff,
+  simp only [rank_le_one_iff, Submodule.isPrincipal_iff, le_antisymm_iff, le_span_singleton_iff,
     span_singleton_le_iff_mem]
   constructor
   · rintro ⟨⟨m, hm⟩, hm'⟩

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Also moved several lemmas into Mathlib/LinearAlgebra/Basis.lean.

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

@@ -345,160 +345,6 @@ theorem exists_mem_ne_zero_of_rank_pos {s : Submodule R M} (h : 0 < Module.rank
   exists_mem_ne_zero_of_ne_bot fun eq => by rw [eq, rank_bot] at h; exact lt_irrefl _ h
 #align exists_mem_ne_zero_of_rank_pos exists_mem_ne_zero_of_rank_pos
 
-/-- A linearly-independent family of vectors in a module over a non-trivial ring must be finite if
-the module is Noetherian. -/
-theorem LinearIndependent.finite_of_isNoetherian [IsNoetherian R M] {v : ι → M}
-    (hv : LinearIndependent R v) : Finite ι := by
-  have hwf := isNoetherian_iff_wellFounded.mp (by infer_instance : IsNoetherian R M)
-  refine' CompleteLattice.WellFounded.finite_of_independent hwf hv.independent_span_singleton
-    fun i contra => _
-  apply hv.ne_zero i
-  have : v i ∈ R ∙ v i := Submodule.mem_span_singleton_self (v i)
-  rwa [contra, Submodule.mem_bot] at this
-#align linear_independent.finite_of_is_noetherian LinearIndependent.finite_of_isNoetherian
-
-theorem LinearIndependent.set_finite_of_isNoetherian [IsNoetherian R M] {s : Set M}
-    (hi : LinearIndependent R ((↑) : s → M)) : s.Finite :=
-  @Set.toFinite _ _ hi.finite_of_isNoetherian
-#align linear_independent.set_finite_of_is_noetherian LinearIndependent.set_finite_of_isNoetherian
-
--- One might hope that a finite spanning set implies that any linearly independent set is finite.
--- While this is true over a division ring
--- (simply because any linearly independent set can be extended to a basis),
--- or over a ring satisfying the strong rank condition
--- (which covers all commutative rings; see `LinearIndependent.finite_of_le_span_finite`).
--- this is not true in general.
--- For example, the left ideal generated by the variables in a noncommutative polynomial ring
--- (`FreeAlgebra R ι`) in infinitely many variables (indexed by `ι`) is free
--- with an infinite basis (consisting of the variables).
--- As another example, for any commutative ring R, the ring of column-finite matrices
--- `Module.End R (ℕ →₀ R)` is isomorphic to `ℕ → Module.End R (ℕ →₀ R)` as a module over itself,
--- which also clearly contains an infinite linearly independent set.
-/--
-Over any nontrivial ring, the existence of a finite spanning set implies that any basis is finite.
--/
-lemma basis_finite_of_finite_spans (w : Set M) (hw : w.Finite) (s : span R w = ⊤) {ι : Type w}
-    (b : Basis ι R M) : Finite ι := by
-  classical
-  haveI := hw.to_subtype
-  cases nonempty_fintype w
-  -- We'll work by contradiction, assuming `ι` is infinite.
-  rw [← not_infinite_iff_finite]
-  intro i
-  -- Let `S` be the union of the supports of `x ∈ w` expressed as linear combinations of `b`.
-  -- This is a finite set since `w` is finite.
-  let S : Finset ι := Finset.univ.sup fun x : w => (b.repr x).support
-  let bS : Set M := b '' S
-  have h : ∀ x ∈ w, x ∈ span R bS := by
-    intro x m
-    rw [← b.total_repr x, Finsupp.span_image_eq_map_total, Submodule.mem_map]
-    use b.repr x
-    simp only [and_true_iff, eq_self_iff_true, Finsupp.mem_supported]
-    change (b.repr x).support ≤ S
-    convert Finset.le_sup (α := Finset ι) (by simp : (⟨x, m⟩ : w) ∈ Finset.univ)
-    rfl
-  -- Thus this finite subset of the basis elements spans the entire module.
-  have k : span R bS = ⊤ := eq_top_iff.2 (le_trans s.ge (span_le.2 h))
-  -- Now there is some `x : ι` not in `S`, since `ι` is infinite.
-  obtain ⟨x, nm⟩ := Infinite.exists_not_mem_finset S
-  -- However it must be in the span of the finite subset,
-  have k' : b x ∈ span R bS := by
-    rw [k]
-    exact mem_top
-  -- giving the desire contradiction.
-  exact b.linearIndependent.not_mem_span_image nm k'
-#align basis_fintype_of_finite_spans basis_finite_of_finite_spansₓ
-
--- From [Les familles libres maximales d'un module ont-elles le meme cardinal?][lazarus1973]
-/-- Over any ring `R`, if `b` is a basis for a module `M`,
-and `s` is a maximal linearly independent set,
-then the union of the supports of `x ∈ s` (when written out in the basis `b`) is all of `b`.
--/
-theorem union_support_maximal_linearIndependent_eq_range_basis {ι : Type w} (b : Basis ι R M)
-    {κ : Type w'} (v : κ → M) (i : LinearIndependent R v) (m : i.Maximal) :
-    ⋃ k, ((b.repr (v k)).support : Set ι) = Set.univ := by
-  -- If that's not the case,
-  by_contra h
-  simp only [← Ne.def, ne_univ_iff_exists_not_mem, mem_iUnion, not_exists_not,
-    Finsupp.mem_support_iff, Finset.mem_coe] at h
-  -- We have some basis element `b b'` which is not in the support of any of the `v i`.
-  obtain ⟨b', w⟩ := h
-  -- Using this, we'll construct a linearly independent family strictly larger than `v`,
-  -- by also using this `b b'`.
-  let v' : Option κ → M := fun o => o.elim (b b') v
-  have r : range v ⊆ range v' := by
-    rintro - ⟨k, rfl⟩
-    use some k
-    rfl
-  have r' : b b' ∉ range v := by
-    rintro ⟨k, p⟩
-    simpa [w] using congr_arg (fun m => (b.repr m) b') p
-  have r'' : range v ≠ range v' := by
-    intro e
-    have p : b b' ∈ range v' := by
-      use none
-      rfl
-    rw [← e] at p
-    exact r' p
-  -- The key step in the proof is checking that this strictly larger family is linearly independent.
-  have i' : LinearIndependent R ((↑) : range v' → M) := by
-    apply LinearIndependent.to_subtype_range
-    rw [linearIndependent_iff]
-    intro l z
-    rw [Finsupp.total_option] at z
-    simp only [Option.elim'] at z
-    change _ + Finsupp.total κ M R v l.some = 0 at z
-    -- We have some linear combination of `b b'` and the `v i`, which we want to show is trivial.
-    -- We'll first show the coefficient of `b b'` is zero,
-    -- by expressing the `v i` in the basis `b`, and using that the `v i` have no `b b'` term.
-    have l₀ : l none = 0 := by
-      rw [← eq_neg_iff_add_eq_zero] at z
-      replace z := neg_eq_iff_eq_neg.mpr z
-      apply_fun fun x => b.repr x b' at z
-      simp only [repr_self, LinearEquiv.map_smul, mul_one, Finsupp.single_eq_same, Pi.neg_apply,
-        Finsupp.smul_single', LinearEquiv.map_neg, Finsupp.coe_neg] at z
-      erw [FunLike.congr_fun (Finsupp.apply_total R (b.repr : M →ₗ[R] ι →₀ R) v l.some) b'] at z
-      simpa [Finsupp.total_apply, w] using z
-    -- Then all the other coefficients are zero, because `v` is linear independent.
-    have l₁ : l.some = 0 := by
-      rw [l₀, zero_smul, zero_add] at z
-      exact linearIndependent_iff.mp i _ z
-    -- Finally we put those facts together to show the linear combination is trivial.
-    ext (_ | a)
-    · simp only [l₀, Finsupp.coe_zero, Pi.zero_apply]
-    · erw [FunLike.congr_fun l₁ a]
-      simp only [Finsupp.coe_zero, Pi.zero_apply]
-  rw [LinearIndependent.Maximal] at m
-  specialize m (range v') i' r
-  exact r'' m
-#align union_support_maximal_linear_independent_eq_range_basis union_support_maximal_linearIndependent_eq_range_basis
-
-/-- Over any ring `R`, if `b` is an infinite basis for a module `M`,
-and `s` is a maximal linearly independent set,
-then the cardinality of `b` is bounded by the cardinality of `s`.
--/
-theorem infinite_basis_le_maximal_linearIndependent' {ι : Type w} (b : Basis ι R M) [Infinite ι]
-    {κ : Type w'} (v : κ → M) (i : LinearIndependent R v) (m : i.Maximal) :
-    Cardinal.lift.{w'} #ι ≤ Cardinal.lift.{w} #κ := by
-  let Φ := fun k : κ => (b.repr (v k)).support
-  have w₁ : #ι ≤ #(Set.range Φ) := by
-    apply Cardinal.le_range_of_union_finset_eq_top
-    exact union_support_maximal_linearIndependent_eq_range_basis b v i m
-  have w₂ : Cardinal.lift.{w'} #(Set.range Φ) ≤ Cardinal.lift.{w} #κ := Cardinal.mk_range_le_lift
-  exact (Cardinal.lift_le.mpr w₁).trans w₂
-#align infinite_basis_le_maximal_linear_independent' infinite_basis_le_maximal_linearIndependent'
-
--- (See `infinite_basis_le_maximal_linearIndependent'` for the more general version
--- where the index types can live in different universes.)
-/-- Over any ring `R`, if `b` is an infinite basis for a module `M`,
-and `s` is a maximal linearly independent set,
-then the cardinality of `b` is bounded by the cardinality of `s`.
--/
-theorem infinite_basis_le_maximal_linearIndependent {ι : Type w} (b : Basis ι R M) [Infinite ι]
-    {κ : Type w} (v : κ → M) (i : LinearIndependent R v) (m : i.Maximal) : #ι ≤ #κ :=
-  Cardinal.lift_le.mp (infinite_basis_le_maximal_linearIndependent' b v i m)
-#align infinite_basis_le_maximal_linear_independent infinite_basis_le_maximal_linearIndependent
-
 theorem CompleteLattice.Independent.subtype_ne_bot_le_rank [NoZeroSMulDivisors R M]
     {V : ι → Submodule R M} (hV : CompleteLattice.Independent V) :
     Cardinal.lift.{v} #{ i : ι // V i ≠ ⊥ } ≤ Cardinal.lift.{w} (Module.rank R M) := by

The dimension of an infinite dimensional dual space is equal to its cardinality. As a consequence (linearEquiv_dual_iff_finiteDimensional), a vector space is isomorphic to its dual iff it's finite dimensional.

The main argument is from https://mathoverflow.net/a/168624. There is a slicker proof in the field case but Vandermonde determinants don't work in a non-commutative ring.

Resolves TODO item posed by Julian Külshammer

• depends on: #8941
• depends on: #8942

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

@@ -108,6 +108,9 @@ protected irreducible_def Module.rank : Cardinal :=
   ⨆ ι : { s : Set V // LinearIndependent K ((↑) : s → V) }, (#ι.1)
 #align module.rank Module.rank
 
+theorem rank_le_card : Module.rank K V ≤ #V :=
+  (Module.rank_def _ _).trans_le (ciSup_le' fun _ ↦ mk_set_le _)
+
 lemma nonempty_linearIndependent_set : Nonempty {s : Set V // LinearIndependent K ((↑) : s → V)} :=
   ⟨⟨∅, linearIndependent_empty _ _⟩⟩
 
@@ -1672,8 +1675,8 @@ theorem rank_finset_sum_le {η} (s : Finset η) (f : η → V →ₗ[K] V') :
 #align linear_map.rank_finset_sum_le LinearMap.rank_finset_sum_le
 
 theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'} :
-    c ≤ rank f ↔ ∃ s : Set V, Cardinal.lift.{v'} #s =
-    Cardinal.lift.{v} c ∧ LinearIndependent K fun x : s => f x := by
+    c ≤ rank f ↔ ∃ s : Set V,
+    Cardinal.lift.{v'} #s = Cardinal.lift.{v} c ∧ LinearIndependent K (fun x : s => f x) := by
   rcases f.rangeRestrict.exists_rightInverse_of_surjective f.range_rangeRestrict with ⟨g, hg⟩
   have fg : LeftInverse f.rangeRestrict g := LinearMap.congr_fun hg
   refine' ⟨fun h => _, _⟩

• Introduce the nondegenerate pairing ((flip_)quotDualCoannihilatorToDual_injective) between M ⧸ W.dualCoannihilator and W . If M is a vector space and W is a finite-dimensional subspace of its dual, this is a perfect pairing (quotDualCoannihilatorToDual_bijective), and W is equal to the annihilator of its coannihilator.

• Use this pairing to show that dualAnnihilator and dualCoannihilator give an antitone order isomorphism orderIsoFiniteCodimDim between finite-codimensional subspaces in a vector space and finite-dimensional subspaces in its dual. This result can be e.g. found in Bourbaki's Algebra. For a finite-dimensional vector space, this gives an OrderIso between all subspaces and all subspaces of the dual.

• Add some lemmas about the image and preimage of annihilators and coannihilators under Dual.eval.

• Expand the docstring of basis_finite_of_finite_spans with comments on generalizations.

• depends on: #8820

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

@@ -362,7 +362,15 @@ theorem LinearIndependent.set_finite_of_isNoetherian [IsNoetherian R M] {s : Set
 -- One might hope that a finite spanning set implies that any linearly independent set is finite.
 -- While this is true over a division ring
 -- (simply because any linearly independent set can be extended to a basis),
--- I'm not certain what more general statements are possible.
+-- or over a ring satisfying the strong rank condition
+-- (which covers all commutative rings; see `LinearIndependent.finite_of_le_span_finite`).
+-- this is not true in general.
+-- For example, the left ideal generated by the variables in a noncommutative polynomial ring
+-- (`FreeAlgebra R ι`) in infinitely many variables (indexed by `ι`) is free
+-- with an infinite basis (consisting of the variables).
+-- As another example, for any commutative ring R, the ring of column-finite matrices
+-- `Module.End R (ℕ →₀ R)` is isomorphic to `ℕ → Module.End R (ℕ →₀ R)` as a module over itself,
+-- which also clearly contains an infinite linearly independent set.
 /--
 Over any nontrivial ring, the existence of a finite spanning set implies that any basis is finite.
 -/

• Rename cardinal_lift_le_rank_of_linearIndependent, cardinal_le_rank_of_linearIndependent('), cardinal_mk/fintype_card/finset_card_le_finrank_of_linearIndependent, fintype_card_le_finrank_of_linearIndependent, finset_card_le_finrank_of_linearIndependent by removing trailing _of_linearIndependent in favor of namespace LinearIndependent.

• Remove cardinal_lift_le_rank_of_linearIndependent', exact duplicate of the version without the prime

• Rename FiniteDimensional/Module.Finite.lt_aleph0_of_linearIndependent to LinearIndependent.lt_aleph0_of_finiteDimensional/finite

• Add one lemma LinearIndependent.aleph0_le_rank in LinearAlgebra/Dimension and two lemmas LinearIndependent.finrank_eq_zero_of_infinite and finrank_eq_nat_card_basis in LinearAlgebra/Finrank

• Remove StrongRankCondition from finrank_eq_zero_of_basis_imp_not_finite and four subsequent lemmas

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

@@ -282,32 +282,39 @@ theorem rank_add_rank_le_rank_prod :
 
 variable {R M M'}
 
-theorem cardinal_lift_le_rank_of_linearIndependent {ι : Type w} {v : ι → M}
+namespace LinearIndependent
+
+theorem cardinal_lift_le_rank {ι : Type w} {v : ι → M}
     (hv : LinearIndependent R v) :
     Cardinal.lift.{v} #ι ≤ Cardinal.lift.{w} (Module.rank R M) := by
-  apply le_trans
-  · exact Cardinal.lift_mk_le'.mpr ⟨(Equiv.ofInjective _ hv.injective).toEmbedding⟩
-  · simp only [Cardinal.lift_le, Module.rank_def]
-    apply le_trans
-    swap
-    · exact le_ciSup (Cardinal.bddAbove_range.{v, v} _) ⟨range v, hv.coe_range⟩
-    · exact le_rfl
-#align cardinal_lift_le_rank_of_linear_independent cardinal_lift_le_rank_of_linearIndependent
+  rw [Module.rank]
+  refine le_trans ?_ (lift_le.mpr <| le_ciSup (bddAbove_range.{v, v} _) ⟨_, hv.coe_range⟩)
+  exact lift_mk_le'.mpr ⟨(Equiv.ofInjective _ hv.injective).toEmbedding⟩
+#align cardinal_lift_le_rank_of_linear_independent LinearIndependent.cardinal_lift_le_rank
+#align cardinal_lift_le_rank_of_linear_independent' LinearIndependent.cardinal_lift_le_rank
 
-theorem cardinal_lift_le_rank_of_linearIndependent' {ι : Type w} {v : ι → M}
-    (hv : LinearIndependent R v) : Cardinal.lift.{v} #ι ≤ Cardinal.lift.{w} (Module.rank R M) :=
-  cardinal_lift_le_rank_of_linearIndependent hv
-#align cardinal_lift_le_rank_of_linear_independent' cardinal_lift_le_rank_of_linearIndependent'
+lemma aleph0_le_rank {ι : Type w} [Infinite ι] {v : ι → M}
+    (hv : LinearIndependent R v) : ℵ₀ ≤ Module.rank R M :=
+  aleph0_le_lift.mp <| (aleph0_le_lift.mpr <| aleph0_le_mk ι).trans hv.cardinal_lift_le_rank
 
-theorem cardinal_le_rank_of_linearIndependent {ι : Type v} {v : ι → M}
+theorem cardinal_le_rank {ι : Type v} {v : ι → M}
     (hv : LinearIndependent R v) : #ι ≤ Module.rank R M := by
-  simpa using cardinal_lift_le_rank_of_linearIndependent hv
-#align cardinal_le_rank_of_linear_independent cardinal_le_rank_of_linearIndependent
+  simpa using hv.cardinal_lift_le_rank
+#align cardinal_le_rank_of_linear_independent LinearIndependent.cardinal_le_rank
 
-theorem cardinal_le_rank_of_linearIndependent' {s : Set M}
+theorem cardinal_le_rank' {s : Set M}
     (hs : LinearIndependent R (fun x => x : s → M)) : #s ≤ Module.rank R M :=
-  cardinal_le_rank_of_linearIndependent hs
-#align cardinal_le_rank_of_linear_independent' cardinal_le_rank_of_linearIndependent'
+  hs.cardinal_le_rank
+#align cardinal_le_rank_of_linear_independent' LinearIndependent.cardinal_le_rank'
+
+end LinearIndependent
+
+@[deprecated]
+alias cardinal_lift_le_rank_of_linearIndependent := LinearIndependent.cardinal_lift_le_rank
+@[deprecated]
+alias cardinal_lift_le_rank_of_linearIndependent' := LinearIndependent.cardinal_lift_le_rank
+@[deprecated] alias cardinal_le_rank_of_linearIndependent := LinearIndependent.cardinal_le_rank
+@[deprecated] alias cardinal_le_rank_of_linearIndependent' := LinearIndependent.cardinal_le_rank'
 
 variable (R M)
 
@@ -491,7 +498,7 @@ theorem CompleteLattice.Independent.subtype_ne_bot_le_rank [NoZeroSMulDivisors R
     exact i.prop
   choose v hvV hv using hI
   have : LinearIndependent R v := (hV.comp Subtype.coe_injective).linearIndependent _ hvV hv
-  exact cardinal_lift_le_rank_of_linearIndependent' this
+  exact this.cardinal_lift_le_rank
 #align complete_lattice.independent.subtype_ne_bot_le_rank CompleteLattice.Independent.subtype_ne_bot_le_rank
 
 end
@@ -526,7 +533,7 @@ theorem rank_pos [Nontrivial M] : 0 < Module.rank R M := by
   suffices 1 ≤ Module.rank R M by exact zero_lt_one.trans_le this
   letI := Module.nontrivial R M
   suffices LinearIndependent R fun y : ({x} : Set M) => (y : M) by
-    simpa using cardinal_le_rank_of_linearIndependent this
+    simpa using this.cardinal_le_rank
   exact linearIndependent_singleton hx
 #align rank_pos rank_pos
 
@@ -543,7 +550,7 @@ lemma rank_eq_zero_iff {R M} [Ring R] [AddCommGroup M] [Module R M] :
     have : LinearIndependent R (fun _ : Unit ↦ x)
     · exact linearIndependent_iff.mpr (fun l hl ↦ Finsupp.unique_ext <| not_not.mp fun H ↦
         hx _ H ((Finsupp.total_unique _ _ _).symm.trans hl))
-    simpa using cardinal_lift_le_rank_of_linearIndependent this
+    simpa using this.cardinal_lift_le_rank
   · intro h
     rw [← le_zero_iff, Module.rank_def]
     apply ciSup_le'
@@ -570,7 +577,7 @@ theorem rank_quotient_eq_of_le_torsion {R M} [CommRing R] [AddCommGroup M] [Modu
     nontriviality R
     rw [Module.rank]
     have := nonempty_linearIndependent_set R M
-    refine ciSup_le fun ⟨s, hs⟩ ↦ cardinal_le_rank_of_linearIndependent (v := (N.mkQ ·)) ?_
+    refine ciSup_le fun ⟨s, hs⟩ ↦ LinearIndependent.cardinal_le_rank (v := (N.mkQ ·)) ?_
     rw [linearIndependent_iff'] at hs ⊢
     simp_rw [← map_smul, ← map_sum, mkQ_apply, Quotient.mk_eq_zero]
     intro t g hg i hi
@@ -1022,8 +1029,7 @@ theorem Basis.card_le_card_of_linearIndependent {ι : Type*} [Fintype ι] (b : B
     {ι' : Type*} [Fintype ι'] {v : ι' → M} (hv : LinearIndependent R v) :
     Fintype.card ι' ≤ Fintype.card ι := by
   letI := nontrivial_of_invariantBasisNumber R
-  simpa [rank_eq_card_basis b, Cardinal.mk_fintype] using
-    cardinal_lift_le_rank_of_linearIndependent' hv
+  simpa [rank_eq_card_basis b, Cardinal.mk_fintype] using hv.cardinal_lift_le_rank
 #align basis.card_le_card_of_linear_independent Basis.card_le_card_of_linearIndependent
 
 theorem Basis.card_le_card_of_submodule (N : Submodule R M) [Fintype ι] (b : Basis ι R M)
@@ -1463,7 +1469,7 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} :
     rcases h with ⟨s, hst, hsc⟩
     exact ⟨s, hsc, (ofVectorSpaceIndex.linearIndependent K V).mono hst⟩
   · rintro ⟨s, rfl, si⟩
-    exact cardinal_le_rank_of_linearIndependent si
+    exact si.cardinal_le_rank
 #align le_rank_iff_exists_linear_independent le_rank_iff_exists_linearIndependent
 
 theorem le_rank_iff_exists_linearIndependent_finset {n : ℕ} : ↑n ≤ Module.rank K V ↔
@@ -1674,7 +1680,7 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'}
   · rintro ⟨s, hsc, si⟩
     have : LinearIndependent K fun x : s => f.rangeRestrict x :=
       LinearIndependent.of_comp f.range.subtype (by convert si)
-    convert cardinal_le_rank_of_linearIndependent this.image
+    convert this.image.cardinal_le_rank
     rw [← Cardinal.lift_inj, ← hsc, Cardinal.mk_image_eq_of_injOn_lift]
     exact injOn_iff_injective.2 this.injective
 #align linear_map.le_rank_iff_exists_linear_independent LinearMap.le_rank_iff_exists_linearIndependent

• Proves that Sup (ciSup) commutes with cardinal addition (ciSup_add_ciSup) and multiplication. Generalize results in Cardinal/Basic introduced in #8842 to achieve this.

• Use ciSup_add_ciSup to prove that the rank of a module is always at least the rank of a submodule plus the rank of the quotient by the submodule. Deduce that the rank of a product module is at least the sum of the ranks of the two factors.

• Show that quotienting by a torsion submodule preserves the rank.

• Golf rank_zero_iff_forall_zero using a recently added lemma.

Co-authored-by: Andrew Yang <the.erd.one@gmail.com>

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

@@ -108,6 +108,9 @@ protected irreducible_def Module.rank : Cardinal :=
   ⨆ ι : { s : Set V // LinearIndependent K ((↑) : s → V) }, (#ι.1)
 #align module.rank Module.rank
 
+lemma nonempty_linearIndependent_set : Nonempty {s : Set V // LinearIndependent K ((↑) : s → V)} :=
+  ⟨⟨∅, linearIndependent_empty _ _⟩⟩
+
 end
 
 section
@@ -145,6 +148,25 @@ theorem rank_le {n : ℕ}
   exact linearIndependent_bounded_of_finset_linearIndependent_bounded H _ li
 #align rank_le rank_le
 
+theorem rank_quotient_add_rank_le [Nontrivial R] (M' : Submodule R M) :
+    Module.rank R (M ⧸ M') + Module.rank R M' ≤ Module.rank R M := by
+  simp_rw [Module.rank_def]
+  have := nonempty_linearIndependent_set R (M ⧸ M')
+  have := nonempty_linearIndependent_set R M'
+  rw [Cardinal.ciSup_add_ciSup _ (bddAbove_range.{v, v} _) _ (bddAbove_range.{v, v} _)]
+  refine ciSup_le fun ⟨s, hs⟩ ↦ ciSup_le fun ⟨t, ht⟩ ↦ ?_
+  choose f hf using Quotient.mk_surjective M'
+  let g : s ⊕ t → M := Sum.elim (f ·) (·)
+  suffices : LinearIndependent R g
+  · refine le_trans ?_ (le_ciSup (bddAbove_range.{v, v} _) ⟨_, this.to_subtype_range⟩)
+    rw [mk_range_eq _ this.injective, mk_sum, lift_id, lift_id]
+  refine .sum_type (.of_comp M'.mkQ ?_) (ht.map' M'.subtype M'.ker_subtype) ?_
+  · convert hs; ext x; exact hf x
+  refine disjoint_def.mpr fun x h₁ h₂ ↦ ?_
+  have : x ∈ M' := span_le.mpr (Set.range_subset_iff.mpr fun i ↦ i.1.2) h₂
+  obtain ⟨c, rfl⟩ := Finsupp.mem_span_range_iff_exists_finsupp.mp h₁
+  simp_rw [← Quotient.mk_eq_zero, ← mkQ_apply, map_finsupp_sum, map_smul, mkQ_apply, hf] at this
+  rw [linearIndependent_iff.mp hs _ this, Finsupp.sum_zero_index]
 
 /-- The rank of the range of a linear map is at most the rank of the source. -/
 -- The proof is: a free submodule of the range lifts to a free submodule of the
@@ -241,6 +263,25 @@ theorem rank_quotient_le (p : Submodule R M) : Module.rank R (M ⧸ p) ≤ Modul
 
 variable [Nontrivial R]
 
+variable (R M M')
+
+open LinearMap in
+theorem lift_rank_add_lift_rank_le_rank_prod :
+    lift.{v'} (Module.rank R M) + lift.{v} (Module.rank R M') ≤ Module.rank R (M × M') := by
+  convert rank_quotient_add_rank_le (ker <| LinearMap.fst R M M')
+  · refine Eq.trans ?_ (lift_id'.{v, v'} _)
+    rw [(quotKerEquivRange _).lift_rank_eq,
+        rank_range_of_surjective _ fst_surjective, lift_umax.{v, v'}]
+  · refine Eq.trans ?_ (lift_id'.{v', v} _)
+    rw [ker_fst, ← (LinearEquiv.ofInjective _ <| inr_injective (M := M) (M₂ := M')).lift_rank_eq,
+        lift_umax.{v', v}]
+
+theorem rank_add_rank_le_rank_prod :
+    Module.rank R M + Module.rank R M₁ ≤ Module.rank R (M × M₁) := by
+  convert ← lift_rank_add_lift_rank_le_rank_prod R M M₁ <;> apply lift_id
+
+variable {R M M'}
+
 theorem cardinal_lift_le_rank_of_linearIndependent {ι : Type w} {v : ι → M}
     (hv : LinearIndependent R v) :
     Cardinal.lift.{v} #ι ≤ Cardinal.lift.{w} (Module.rank R M) := by
@@ -491,18 +532,6 @@ theorem rank_pos [Nontrivial M] : 0 < Module.rank R M := by
 
 variable [Nontrivial R]
 
-theorem rank_zero_iff_forall_zero : Module.rank R M = 0 ↔ ∀ x : M, x = 0 := by
-  refine' ⟨fun h => _, fun h => _⟩
-  · contrapose! h
-    obtain ⟨x, hx⟩ := h
-    letI : Nontrivial M := nontrivial_of_ne _ _ hx
-    exact rank_pos.ne'
-  · have : (⊤ : Submodule R M) = ⊥ := by
-      ext x
-      simp [h x]
-    rw [← rank_top, this, rank_bot]
-#align rank_zero_iff_forall_zero rank_zero_iff_forall_zero
-
 /-- See `rank_zero_iff` for a stronger version with `NoZeroSMulDivisor R M`. -/
 lemma rank_eq_zero_iff {R M} [Ring R] [AddCommGroup M] [Module R M] :
     Module.rank R M = 0 ↔ ∀ x : M, ∃ a : R, a ≠ 0 ∧ a • x = 0 := by
@@ -525,11 +554,30 @@ lemma rank_eq_zero_iff {R M} [Ring R] [AddCommGroup M] [Module R M] :
     apply ha
     simpa using FunLike.congr_fun (linearIndependent_iff.mp hs (Finsupp.single i a) (by simpa)) i
 
+theorem rank_zero_iff_forall_zero : Module.rank R M = 0 ↔ ∀ x : M, x = 0 := by
+  simp_rw [rank_eq_zero_iff, smul_eq_zero, and_or_left, not_and_self_iff, false_or,
+    exists_and_right, and_iff_right (exists_ne (0 : R))]
+#align rank_zero_iff_forall_zero rank_zero_iff_forall_zero
+
 lemma rank_eq_zero_iff_isTorsion {R M} [CommRing R] [IsDomain R] [AddCommGroup M] [Module R M] :
     Module.rank R M = 0 ↔ Module.IsTorsion R M := by
   rw [Module.IsTorsion, rank_eq_zero_iff]
   simp [mem_nonZeroDivisors_iff_ne_zero]
 
+theorem rank_quotient_eq_of_le_torsion {R M} [CommRing R] [AddCommGroup M] [Module R M]
+    {N : Submodule R M} (hN : N ≤ torsion R M) : Module.rank R (M ⧸ N) = Module.rank R M :=
+  (rank_quotient_le N).antisymm <| by
+    nontriviality R
+    rw [Module.rank]
+    have := nonempty_linearIndependent_set R M
+    refine ciSup_le fun ⟨s, hs⟩ ↦ cardinal_le_rank_of_linearIndependent (v := (N.mkQ ·)) ?_
+    rw [linearIndependent_iff'] at hs ⊢
+    simp_rw [← map_smul, ← map_sum, mkQ_apply, Quotient.mk_eq_zero]
+    intro t g hg i hi
+    obtain ⟨r, hg⟩ := hN hg
+    simp_rw [Finset.smul_sum, Submonoid.smul_def, smul_smul] at hg
+    exact r.prop _ (mul_comm (g i) r ▸ hs t _ hg i hi)
+
 /-- See `rank_subsingleton` for the reason that `Nontrivial R` is needed.
 Also see `rank_eq_zero_iff` for the version without `NoZeroSMulDivisor R M`. -/
 theorem rank_zero_iff : Module.rank R M = 0 ↔ Subsingleton M :=

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

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

Also add the Algebra versions of these results.

@@ -547,6 +547,142 @@ theorem rank_pos_iff_nontrivial : 0 < Module.rank R M ↔ Nontrivial M :=
 
 end RankZero
 
+section SurjectiveInjective
+
+section Module
+
+variable {R : Type w} {M : Type v} [Ring R] [AddCommGroup M] [Module R M]
+  {R' : Type w'} {M' : Type v'} [Ring R'] [AddCommGroup M'] [Module R' M']
+
+/-- If `M / R` and `M' / R'` are modules, `i : R' → R` is a map which sends non-zero elements to
+non-zero elements, `j : M →+ M'` is an injective group homomorphism, such that the scalar
+multiplications on `M` and `M'` are compatible, then the rank of `M / R` is smaller than or equal to
+the rank of `M' / R'`. As a special case, taking `R = R'` it is
+`LinearMap.lift_rank_le_of_injective`. -/
+theorem lift_rank_le_of_injective_injective (i : R' → R) (j : M →+ M')
+    (hi : ∀ r, i r = 0 → r = 0) (hj : Injective j)
+    (hc : ∀ (r : R') (m : M), j (i r • m) = r • j m) :
+    lift.{v'} (Module.rank R M) ≤ lift.{v} (Module.rank R' M') := by
+  simp_rw [Module.rank, lift_iSup (bddAbove_range.{v', v'} _), lift_iSup (bddAbove_range.{v, v} _)]
+  exact ciSup_mono' (bddAbove_range.{v', v} _) fun ⟨s, h⟩ ↦ ⟨⟨j '' s,
+    (h.map_of_injective_injective i j hi (fun _ _ ↦ hj <| by rwa [j.map_zero]) hc).image⟩,
+      lift_mk_le'.mpr ⟨(Equiv.Set.image j s hj).toEmbedding⟩⟩
+
+/-- If `M / R` and `M' / R'` are modules, `i : R → R'` is a surjective map which maps zero to zero,
+`j : M →+ M'` is an injective group homomorphism, such that the scalar multiplications on `M` and
+`M'` are compatible, then the rank of `M / R` is smaller than or equal to the rank of `M' / R'`.
+As a special case, taking `R = R'` it is `LinearMap.lift_rank_le_of_injective`. -/
+theorem lift_rank_le_of_surjective_injective (i : ZeroHom R R') (j : M →+ M')
+    (hi : Surjective i) (hj : Injective j) (hc : ∀ (r : R) (m : M), j (r • m) = i r • j m) :
+    lift.{v'} (Module.rank R M) ≤ lift.{v} (Module.rank R' M') := by
+  obtain ⟨i', hi'⟩ := hi.hasRightInverse
+  refine lift_rank_le_of_injective_injective i' j (fun _ h ↦ ?_) hj fun r m ↦ ?_
+  · apply_fun i at h
+    rwa [hi', i.map_zero] at h
+  rw [hc (i' r) m, hi']
+
+/-- If `M / R` and `M' / R'` are modules, `i : R → R'` is a bijective map which maps zero to zero,
+`j : M ≃+ M'` is a group isomorphism, such that the scalar multiplications on `M` and `M'` are
+compatible, then the rank of `M / R` is equal to the rank of `M' / R'`.
+As a special case, taking `R = R'` it is `LinearEquiv.lift_rank_eq`. -/
+theorem lift_rank_eq_of_equiv_equiv (i : ZeroHom R R') (j : M ≃+ M')
+    (hi : Bijective i) (hc : ∀ (r : R) (m : M), j (r • m) = i r • j m) :
+    lift.{v'} (Module.rank R M) = lift.{v} (Module.rank R' M') :=
+  (lift_rank_le_of_surjective_injective i j hi.2 j.injective hc).antisymm <|
+    lift_rank_le_of_injective_injective i j.symm (fun _ _ ↦ hi.1 <| by rwa [i.map_zero])
+      j.symm.injective fun _ _ ↦ j.symm_apply_eq.2 <| by erw [hc, j.apply_symm_apply]
+
+variable {M' : Type v} [Ring R'] [AddCommGroup M'] [Module R' M']
+
+/-- The same-universe version of `lift_rank_le_of_injective_injective`. -/
+theorem rank_le_of_injective_injective (i : R' → R) (j : M →+ M')
+    (hi : ∀ r, i r = 0 → r = 0) (hj : Injective j)
+    (hc : ∀ (r : R') (m : M), j (i r • m) = r • j m) :
+    Module.rank R M ≤ Module.rank R' M' := by
+  simpa only [lift_id] using lift_rank_le_of_injective_injective i j hi hj hc
+
+/-- The same-universe version of `lift_rank_le_of_surjective_injective`. -/
+theorem rank_le_of_surjective_injective (i : ZeroHom R R') (j : M →+ M')
+    (hi : Surjective i) (hj : Injective j)
+    (hc : ∀ (r : R) (m : M), j (r • m) = i r • j m) :
+    Module.rank R M ≤ Module.rank R' M' := by
+  simpa only [lift_id] using lift_rank_le_of_surjective_injective i j hi hj hc
+
+/-- The same-universe version of `lift_rank_eq_of_equiv_equiv`. -/
+theorem rank_eq_of_equiv_equiv (i : ZeroHom R R') (j : M ≃+ M')
+    (hi : Bijective i) (hc : ∀ (r : R) (m : M), j (r • m) = i r • j m) :
+    Module.rank R M = Module.rank R' M' := by
+  simpa only [lift_id] using lift_rank_eq_of_equiv_equiv i j hi hc
+
+end Module
+
+namespace Algebra
+
+variable {R : Type w} {S : Type v} [CommRing R] [Ring S] [Algebra R S]
+  {R' : Type w'} {S' : Type v'} [CommRing R'] [Ring S'] [Algebra R' S']
+
+/-- If `S / R` and `S' / R'` are algebras, `i : R' →+* R` and `j : S →+* S'` are injective ring
+homorphisms, such that `R' → R → S → S'` and `R' → S'` commute, then the rank of `S / R` is
+smaller than or equal to the rank of `S' / R'`. -/
+theorem lift_rank_le_of_injective_injective
+    (i : R' →+* R) (j : S →+* S') (hi : Injective i) (hj : Injective j)
+    (hc : (j.comp (algebraMap R S)).comp i = algebraMap R' S') :
+    lift.{v'} (Module.rank R S) ≤ lift.{v} (Module.rank R' S') := by
+  refine _root_.lift_rank_le_of_injective_injective i j
+    (fun _ _ ↦ hi <| by rwa [i.map_zero]) hj fun r _ ↦ ?_
+  have := congr($hc r)
+  simp only [RingHom.coe_comp, comp_apply] at this
+  simp_rw [smul_def, AddMonoidHom.coe_coe, map_mul, this]
+
+/-- If `S / R` and `S' / R'` are algebras, `i : R →+* R'` is a surjective ring homomorphism,
+`j : S →+* S'` is an injective ring homorphism, such that `R → R' → S'` and `R → S → S'` commute,
+then the rank of `S / R` is smaller than or equal to the rank of `S' / R'`. -/
+theorem lift_rank_le_of_surjective_injective
+    (i : R →+* R') (j : S →+* S') (hi : Surjective i) (hj : Injective j)
+    (hc : (algebraMap R' S').comp i = j.comp (algebraMap R S)) :
+    lift.{v'} (Module.rank R S) ≤ lift.{v} (Module.rank R' S') := by
+  refine _root_.lift_rank_le_of_surjective_injective i j hi hj fun r _ ↦ ?_
+  have := congr($hc r)
+  simp only [RingHom.coe_comp, comp_apply] at this
+  simp only [smul_def, AddMonoidHom.coe_coe, map_mul, ZeroHom.coe_coe, this]
+
+/-- If `S / R` and `S' / R'` are algebras, `i : R ≃+* R'` and `j : S ≃+* S'` are
+ring isomorphisms, such that `R → R' → S'` and `R → S → S'` commute,
+then the rank of `S / R` is equal to the rank of `S' / R'`. -/
+theorem lift_rank_eq_of_equiv_equiv (i : R ≃+* R') (j : S ≃+* S')
+    (hc : (algebraMap R' S').comp i.toRingHom = j.toRingHom.comp (algebraMap R S)) :
+    lift.{v'} (Module.rank R S) = lift.{v} (Module.rank R' S') := by
+  refine _root_.lift_rank_eq_of_equiv_equiv i j i.bijective fun r _ ↦ ?_
+  have := congr($hc r)
+  simp only [RingEquiv.toRingHom_eq_coe, RingHom.coe_comp, RingHom.coe_coe, comp_apply] at this
+  simp only [smul_def, RingEquiv.coe_toAddEquiv, map_mul, ZeroHom.coe_coe, this]
+
+variable {S' : Type v} [CommRing R'] [Ring S'] [Algebra R' S']
+
+/-- The same-universe version of `Algebra.lift_rank_le_of_injective_injective`. -/
+theorem rank_le_of_injective_injective
+    (i : R' →+* R) (j : S →+* S') (hi : Injective i) (hj : Injective j)
+    (hc : (j.comp (algebraMap R S)).comp i = algebraMap R' S') :
+    Module.rank R S ≤ Module.rank R' S' := by
+  simpa only [lift_id] using lift_rank_le_of_injective_injective i j hi hj hc
+
+/-- The same-universe version of `Algebra.lift_rank_le_of_surjective_injective`. -/
+theorem rank_le_of_surjective_injective
+    (i : R →+* R') (j : S →+* S') (hi : Surjective i) (hj : Injective j)
+    (hc : (algebraMap R' S').comp i = j.comp (algebraMap R S)) :
+    Module.rank R S ≤ Module.rank R' S' := by
+  simpa only [lift_id] using lift_rank_le_of_surjective_injective i j hi hj hc
+
+/-- The same-universe version of `Algebra.lift_rank_eq_of_equiv_equiv`. -/
+theorem rank_eq_of_equiv_equiv (i : R ≃+* R') (j : S ≃+* S')
+    (hc : (algebraMap R' S').comp i.toRingHom = j.toRingHom.comp (algebraMap R S)) :
+    Module.rank R S = Module.rank R' S' := by
+  simpa only [lift_id] using lift_rank_eq_of_equiv_equiv i j hc
+
+end Algebra
+
+end SurjectiveInjective
+
 section InvariantBasisNumber
 
 variable {R : Type u} [Ring R] [InvariantBasisNumber R]

From the Hairer challenge

• add flip_in/sur/bijective_iff₁₂: if either of the spaces V and W is finite-dimensional, a linear map V → W* is injective/surjective/bijective iff the flipped map W → V* is surjective/injective/bijective.

• also add consequence for SeparatingDual from the projective space thread (cc @smorel394)

• remove the FiniteDimensional condition from dual_finrank_eq, finrank_range_dualMap_eq_finrank_range, and dualMap_injective/bijective_iff, completing two TODO items by @kmill

• add two lemmas toDual_injective and finite_dual_iff

• golf several proofs in LinearAlgebra/Dual

Co-authored-by: Kyle Miller <kmill31415@gmail.com>

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

@@ -128,7 +128,7 @@ theorem LinearMap.lift_rank_le_of_injective (f : M →ₗ[R] M') (i : Injective
   apply ciSup_mono' (Cardinal.bddAbove_range.{v', v} _)
   rintro ⟨s, li⟩
   refine' ⟨⟨f '' s, _⟩, Cardinal.lift_mk_le'.mpr ⟨(Equiv.Set.image f s i).toEmbedding⟩⟩
-  exact (li.map' _ <| LinearMap.ker_eq_bot.mpr i).image
+  exact (li.map' _ <| LinearMap.ker_eq_bot_of_injective i).image
 #align linear_map.lift_rank_le_of_injective LinearMap.lift_rank_le_of_injective
 
 theorem LinearMap.rank_le_of_injective (f : M →ₗ[R] M₁) (i : Injective f) :
@@ -347,8 +347,7 @@ lemma basis_finite_of_finite_spans (w : Set M) (hw : w.Finite) (s : span R w = 
     rw [k]
     exact mem_top
   -- giving the desire contradiction.
-  refine' b.linearIndependent.not_mem_span_image _ k'
-  exact nm
+  exact b.linearIndependent.not_mem_span_image nm k'
 #align basis_fintype_of_finite_spans basis_finite_of_finite_spansₓ
 
 -- From [Les familles libres maximales d'un module ont-elles le meme cardinal?][lazarus1973]
@@ -382,18 +381,10 @@ theorem union_support_maximal_linearIndependent_eq_range_basis {ι : Type w} (b
       rfl
     rw [← e] at p
     exact r' p
-  have inj' : Injective v' := by
-    rintro (_ | k) (_ | k) z
-    · rfl
-    · exfalso
-      exact r' ⟨k, z.symm⟩
-    · exfalso
-      exact r' ⟨k, z⟩
-    · congr
-      exact i.injective z
   -- The key step in the proof is checking that this strictly larger family is linearly independent.
   have i' : LinearIndependent R ((↑) : range v' → M) := by
-    rw [linearIndependent_subtype_range inj', linearIndependent_iff]
+    apply LinearIndependent.to_subtype_range
+    rw [linearIndependent_iff]
     intro l z
     rw [Finsupp.total_option] at z
     simp only [Option.elim'] at z
@@ -418,7 +409,7 @@ theorem union_support_maximal_linearIndependent_eq_range_basis {ι : Type w} (b
     · simp only [l₀, Finsupp.coe_zero, Pi.zero_apply]
     · erw [FunLike.congr_fun l₁ a]
       simp only [Finsupp.coe_zero, Pi.zero_apply]
-  dsimp [LinearIndependent.Maximal] at m
+  rw [LinearIndependent.Maximal] at m
   specialize m (range v') i' r
   exact r'' m
 #align union_support_maximal_linear_independent_eq_range_basis union_support_maximal_linearIndependent_eq_range_basis
@@ -709,14 +700,15 @@ then any linearly independent family `v : ι → M`
 contained in the span of some finite `w : Set M`,
 is itself finite.
 -/
-def linearIndependentFintypeOfLeSpanFintype {ι : Type*} (v : ι → M) (i : LinearIndependent R v)
-    (w : Set M) [Fintype w] (s : range v ≤ span R w) : Fintype ι :=
-  fintypeOfFinsetCardLe (Fintype.card w) fun t => by
+lemma LinearIndependent.finite_of_le_span_finite {ι : Type*} (v : ι → M) (i : LinearIndependent R v)
+    (w : Set M) [Finite w] (s : range v ≤ span R w) : Finite ι :=
+  letI := Fintype.ofFinite w
+  Fintype.finite <| fintypeOfFinsetCardLe (Fintype.card w) fun t => by
     let v' := fun x : (t : Set ι) => v x
     have i' : LinearIndependent R v' := i.comp _ Subtype.val_injective
     have s' : range v' ≤ span R w := (range_comp_subset_range _ _).trans s
     simpa using linearIndependent_le_span_aux' v' i' w s'
-#align linear_independent_fintype_of_le_span_fintype linearIndependentFintypeOfLeSpanFintype
+#align linear_independent_fintype_of_le_span_fintype LinearIndependent.finite_of_le_span_finite
 
 /-- If `R` satisfies the strong rank condition,
 then for any linearly independent family `v : ι → M`
@@ -725,7 +717,8 @@ the cardinality of `ι` is bounded by the cardinality of `w`.
 -/
 theorem linearIndependent_le_span' {ι : Type*} (v : ι → M) (i : LinearIndependent R v) (w : Set M)
     [Fintype w] (s : range v ≤ span R w) : #ι ≤ Fintype.card w := by
-  haveI : Fintype ι := linearIndependentFintypeOfLeSpanFintype v i w s
+  haveI : Finite ι := i.finite_of_le_span_finite v w s
+  letI := Fintype.ofFinite ι
   rw [Cardinal.mk_fintype]
   simp only [Cardinal.natCast_le]
   exact linearIndependent_le_span_aux' v i w s
@@ -761,8 +754,8 @@ theorem linearIndependent_le_infinite_basis {ι : Type w} (b : Basis ι R M) [In
   obtain ⟨s, w : Infinite ↑(Φ ⁻¹' {s})⟩ := Cardinal.exists_infinite_fiber Φ h (by infer_instance)
   let v' := fun k : Φ ⁻¹' {s} => v k
   have i' : LinearIndependent R v' := i.comp _ Subtype.val_injective
-  have w' : Fintype (Φ ⁻¹' {s}) := by
-    apply linearIndependentFintypeOfLeSpanFintype v' i' (s.image b)
+  have w' : Finite (Φ ⁻¹' {s}) := by
+    apply i'.finite_of_le_span_finite v' (s.image b)
     rintro m ⟨⟨p, ⟨rfl⟩⟩, rfl⟩
     simp only [SetLike.mem_coe, Subtype.coe_mk, Finset.coe_image]
     apply Basis.mem_span_repr_support
@@ -907,10 +900,11 @@ theorem rank_span_set {s : Set M} (hs : LinearIndependent R (fun x => x : s →
 finite free module `M`. A property is true for all submodules of `M` if it satisfies the following
 "inductive step": the property is true for a submodule `N` if it's true for all submodules `N'`
 of `N` with the property that there exists `0 ≠ x ∈ N` such that the sum `N' + Rx` is direct. -/
-def Submodule.inductionOnRank [IsDomain R] [Fintype ι] (b : Basis ι R M)
+def Submodule.inductionOnRank [IsDomain R] [Finite ι] (b : Basis ι R M)
     (P : Submodule R M → Sort*) (ih : ∀ N : Submodule R M,
     (∀ N' ≤ N, ∀ x ∈ N, (∀ (c : R), ∀ y ∈ N', c • x + y = (0 : M) → c = 0) → P N') → P N)
     (N : Submodule R M) : P N :=
+  letI := Fintype.ofFinite ι
   Submodule.inductionOnRankAux b P ih (Fintype.card ι) N fun hs hli => by
     simpa using b.card_le_card_of_linearIndependent hli
 #align submodule.induction_on_rank Submodule.inductionOnRank

A portion of results in Mathlib/LinearAlgebra/FiniteDimensional.lean were generalized to rings and moved to Mathlib/LinearAlgebra/FreeModule/Finite/Rank.lean. Most API lemmas for FiniteDimensional are kept but replaced with one lemma proofs. Definitions and niche lemmas are replaced by the generalized version completely.

Co-authored-by: erd1 <the.erd.one@gmail.com> Co-authored-by: Andrew Yang <the.erd.one@gmail.com>

@@ -5,6 +5,7 @@ Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 -/
 import Mathlib.Algebra.Module.BigOperators
 import Mathlib.LinearAlgebra.Basis.VectorSpace
+import Mathlib.Algebra.Module.Torsion
 import Mathlib.LinearAlgebra.DFinsupp
 import Mathlib.LinearAlgebra.FreeModule.Basic
 import Mathlib.LinearAlgebra.InvariantBasisNumber
@@ -78,7 +79,7 @@ noncomputable section
 
 universe u v v' v'' u₁' w w'
 
-variable {K : Type u} {V V₁ V₂ V₃ : Type v} {V' V'₁ : Type v'} {V'' : Type v''}
+variable {K R : Type u} {V V₁ V₂ V₃ : Type v} {V' V'₁ : Type v'} {V'' : Type v''}
 
 variable {ι : Type w} {ι' : Type w'} {η : Type u₁'} {φ : η → Type*}
 
@@ -102,8 +103,6 @@ this is the same as the dimension of the space (i.e. the cardinality of any basi
 
 In particular this agrees with the usual notion of the dimension of a vector space.
 
-The definition is marked as protected to avoid conflicts with `_root_.rank`,
-the rank of a linear map.
 -/
 protected irreducible_def Module.rank : Cardinal :=
   ⨆ ι : { s : Set V // LinearIndependent K ((↑) : s → V) }, (#ι.1)
@@ -113,7 +112,7 @@ end
 
 section
 
-variable {R : Type u} [Ring R]
+variable [Ring R]
 
 variable {M : Type v} [AddCommGroup M] [Module R M]
 
@@ -471,7 +470,7 @@ variable {R : Type u} {M : Type v}
 
 variable [Ring R] [AddCommGroup M] [Module R M]
 
-@[simp]
+@[nontriviality, simp]
 theorem rank_subsingleton [Subsingleton R] : Module.rank R M = 1 := by
   haveI := Module.subsingleton R M
   have : Nonempty { s : Set M // LinearIndependent R ((↑) : s → M) } :=
@@ -513,7 +512,35 @@ theorem rank_zero_iff_forall_zero : Module.rank R M = 0 ↔ ∀ x : M, x = 0 :=
     rw [← rank_top, this, rank_bot]
 #align rank_zero_iff_forall_zero rank_zero_iff_forall_zero
 
-/-- See `rank_subsingleton` for the reason that `Nontrivial R` is needed. -/
+/-- See `rank_zero_iff` for a stronger version with `NoZeroSMulDivisor R M`. -/
+lemma rank_eq_zero_iff {R M} [Ring R] [AddCommGroup M] [Module R M] :
+    Module.rank R M = 0 ↔ ∀ x : M, ∃ a : R, a ≠ 0 ∧ a • x = 0 := by
+  nontriviality R
+  constructor
+  · contrapose!
+    rintro ⟨x, hx⟩
+    rw [← Cardinal.one_le_iff_ne_zero]
+    have : LinearIndependent R (fun _ : Unit ↦ x)
+    · exact linearIndependent_iff.mpr (fun l hl ↦ Finsupp.unique_ext <| not_not.mp fun H ↦
+        hx _ H ((Finsupp.total_unique _ _ _).symm.trans hl))
+    simpa using cardinal_lift_le_rank_of_linearIndependent this
+  · intro h
+    rw [← le_zero_iff, Module.rank_def]
+    apply ciSup_le'
+    intro ⟨s, hs⟩
+    rw [nonpos_iff_eq_zero, Cardinal.mk_eq_zero_iff, ← not_nonempty_iff]
+    rintro ⟨i : s⟩
+    obtain ⟨a, ha, ha'⟩ := h i
+    apply ha
+    simpa using FunLike.congr_fun (linearIndependent_iff.mp hs (Finsupp.single i a) (by simpa)) i
+
+lemma rank_eq_zero_iff_isTorsion {R M} [CommRing R] [IsDomain R] [AddCommGroup M] [Module R M] :
+    Module.rank R M = 0 ↔ Module.IsTorsion R M := by
+  rw [Module.IsTorsion, rank_eq_zero_iff]
+  simp [mem_nonZeroDivisors_iff_ne_zero]
+
+/-- See `rank_subsingleton` for the reason that `Nontrivial R` is needed.
+Also see `rank_eq_zero_iff` for the version without `NoZeroSMulDivisor R M`. -/
 theorem rank_zero_iff : Module.rank R M = 0 ↔ Subsingleton M :=
   rank_zero_iff_forall_zero.trans (subsingleton_iff_forall_eq 0).symm
 #align rank_zero_iff rank_zero_iff
@@ -1071,9 +1098,9 @@ end Free
 
 section DivisionRing
 
-variable [DivisionRing K]
+variable [DivisionRing K] [Ring R] [StrongRankCondition R]
 
-variable [AddCommGroup V] [Module K V]
+variable [AddCommGroup V] [Module K V] [Module R V]
 
 variable [AddCommGroup V'] [Module K V']
 
@@ -1086,19 +1113,25 @@ theorem Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0 (h : Module.rank K V <
 #align basis.finite_of_vector_space_index_of_rank_lt_aleph_0 Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0
 
 -- TODO how far can we generalise this?
--- When `s` is finite, we could prove this for any ring satisfying the strong rank condition
--- using `linearIndependent_le_span'`
 theorem rank_span_le (s : Set V) : Module.rank K (span K s) ≤ #s := by
   obtain ⟨b, hb, hsab, hlib⟩ := exists_linearIndependent K s
   convert Cardinal.mk_le_mk_of_subset hb
   rw [← hsab, rank_span_set hlib]
 #align rank_span_le rank_span_le
 
-theorem rank_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V)) < ℵ₀ :=
-  calc
-    Module.rank K (span K (↑s : Set V)) ≤ #(↑s : Set V) := rank_span_le (s : Set V)
-    _ = s.card := by rw [Finset.coe_sort_coe, Cardinal.mk_coe_finset]
-    _ < ℵ₀ := Cardinal.nat_lt_aleph0 _
+theorem rank_span_le_of_finite {s : Set V} (hs : s.Finite) : Module.rank R (span R s) ≤ #s := by
+  rw [Module.rank_def]
+  apply ciSup_le'
+  rintro ⟨t, ht⟩
+  letI := hs.fintype
+  simpa [Cardinal.mk_image_eq Subtype.val_injective] using linearIndependent_le_span' _
+    (ht.map (f := Submodule.subtype _) (by simp)).image s (fun x ↦ by aesop)
+
+theorem rank_span_finset_le (s : Finset V) : Module.rank R (span R (s : Set V)) ≤ s.card := by
+  simpa using rank_span_le_of_finite s.finite_toSet
+
+theorem rank_span_of_finset (s : Finset V) : Module.rank R (span R (s : Set V)) < ℵ₀ :=
+  (rank_span_finset_le s).trans_lt (Cardinal.nat_lt_aleph0 _)
 #align rank_span_of_finset rank_span_of_finset
 
 theorem rank_quotient_add_rank (p : Submodule K V) :

@@ -1108,7 +1108,7 @@ theorem rank_quotient_add_rank (p : Submodule K V) :
     exact rank_prod'.symm.trans f.rank_eq
 #align rank_quotient_add_rank rank_quotient_add_rank
 
-/-- rank-nullity theorem -/
+/-- The **rank-nullity theorem** -/
 theorem rank_range_add_rank_ker (f : V →ₗ[K] V₁) :
     Module.rank K (LinearMap.range f) + Module.rank K (LinearMap.ker f) = Module.rank K V := by
   haveI := fun p : Submodule K V => Classical.decEq (V ⧸ p)

This matches Set.inclusion, Subring.inclusion, Subalgebra.inclusion, etc.

Also renames the homOfLe spellings in Algebra/Lie to match.

Note that we leave LieSubalgebra.ofLe, as this is a completely different statement!

As requested by @alreadydone.

@@ -181,7 +181,7 @@ theorem rank_map_le (f : M →ₗ[R] M₁) (p : Submodule R M) :
 
 theorem rank_le_of_submodule (s t : Submodule R M) (h : s ≤ t) :
     Module.rank R s ≤ Module.rank R t :=
-  (ofLe h).rank_le_of_injective fun ⟨x, _⟩ ⟨y, _⟩ eq =>
+  (Submodule.inclusion h).rank_le_of_injective fun ⟨x, _⟩ ⟨y, _⟩ eq =>
     Subtype.eq <| show x = y from Subtype.ext_iff_val.1 eq
 #align rank_le_of_submodule rank_le_of_submodule
 
@@ -830,7 +830,7 @@ theorem Basis.card_le_card_of_submodule (N : Submodule R M) [Fintype ι] (b : Ba
 theorem Basis.card_le_card_of_le {N O : Submodule R M} (hNO : N ≤ O) [Fintype ι] (b : Basis ι R O)
     [Fintype ι'] (b' : Basis ι' R N) : Fintype.card ι' ≤ Fintype.card ι :=
   b.card_le_card_of_linearIndependent
-    (b'.linearIndependent.map' (Submodule.ofLe hNO) (N.ker_ofLe O _))
+    (b'.linearIndependent.map' (Submodule.inclusion hNO) (N.ker_inclusion O _))
 #align basis.card_le_card_of_le Basis.card_le_card_of_le
 
 theorem Basis.mk_eq_rank (v : Basis ι R M) :
@@ -1198,12 +1198,14 @@ theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd
 theorem Submodule.rank_sup_add_rank_inf_eq (s t : Submodule K V) :
     Module.rank K (s ⊔ t : Submodule K V) + Module.rank K (s ⊓ t : Submodule K V) =
     Module.rank K s + Module.rank K t :=
-  rank_add_rank_split (ofLe le_sup_left) (ofLe le_sup_right) (ofLe inf_le_left) (ofLe inf_le_right)
+  rank_add_rank_split
+    (inclusion le_sup_left) (inclusion le_sup_right)
+    (inclusion inf_le_left) (inclusion inf_le_right)
     (by
       rw [← map_le_map_iff' (ker_subtype <| s ⊔ t), Submodule.map_sup, Submodule.map_top, ←
-        LinearMap.range_comp, ← LinearMap.range_comp, subtype_comp_ofLe, subtype_comp_ofLe,
-        range_subtype, range_subtype, range_subtype])
-    (ker_ofLe _ _ _) (by ext ⟨x, hx⟩; rfl)
+        LinearMap.range_comp, ← LinearMap.range_comp, subtype_comp_inclusion,
+        subtype_comp_inclusion, range_subtype, range_subtype, range_subtype])
+    (ker_inclusion _ _ _) (by ext ⟨x, hx⟩; rfl)
     (by
       rintro ⟨b₁, hb₁⟩ ⟨b₂, hb₂⟩ eq
       obtain rfl : b₁ = b₂ := congr_arg Subtype.val eq

We have turned to Type* instead of Type _, but many of them remained in mathlib because the straight replacement did not work. In general, having Type _ before the colon is a code smell, though, as it hides which types should be in the same universe and which shouldn't, and is not very robust.

This PR replaces most of the remaining Type _ before the colon (except those in category theory) by Type* or Type u. This has uncovered a few bugs (where declarations were not as polymorphic as they should be).

I had to increase heartbeats at two places when replacing Type _ by Type*, but I think it's worth it as it's really more robust.

@@ -725,7 +725,7 @@ theorem linearIndependent_le_span_finset {ι : Type*} (v : ι → M) (i : Linear
 /-- An auxiliary lemma for `linearIndependent_le_basis`:
 we handle the case where the basis `b` is infinite.
 -/
-theorem linearIndependent_le_infinite_basis {ι : Type*} (b : Basis ι R M) [Infinite ι] {κ : Type _}
+theorem linearIndependent_le_infinite_basis {ι : Type w} (b : Basis ι R M) [Infinite ι] {κ : Type w}
     (v : κ → M) (i : LinearIndependent R v) : #κ ≤ #ι := by
   classical
   by_contra h
@@ -747,7 +747,7 @@ if `b` is a basis for a module `M`,
 and `s` is a linearly independent set,
 then the cardinality of `s` is bounded by the cardinality of `b`.
 -/
-theorem linearIndependent_le_basis {ι : Type*} (b : Basis ι R M) {κ : Type _} (v : κ → M)
+theorem linearIndependent_le_basis {ι : Type w} (b : Basis ι R M) {κ : Type w} (v : κ → M)
     (i : LinearIndependent R v) : #κ ≤ #ι := by
   classical
   -- We split into cases depending on whether `ι` is infinite.
@@ -775,8 +775,8 @@ then every maximal linearly independent set has the same cardinality as `b`.
 This proof (along with some of the lemmas above) comes from
 [Les familles libres maximales d'un module ont-elles le meme cardinal?][lazarus1973]
 -/
-theorem maximal_linearIndependent_eq_infinite_basis {ι : Type*} (b : Basis ι R M) [Infinite ι]
-    {κ : Type _} (v : κ → M) (i : LinearIndependent R v) (m : i.Maximal) : #κ = #ι := by
+theorem maximal_linearIndependent_eq_infinite_basis {ι : Type w} (b : Basis ι R M) [Infinite ι]
+    {κ : Type w} (v : κ → M) (i : LinearIndependent R v) (m : i.Maximal) : #κ = #ι := by
   apply le_antisymm
   · exact linearIndependent_le_basis b v i
   · haveI : Nontrivial R := nontrivial_of_invariantBasisNumber R

This will improve spaces in the mathlib4 docs.

@@ -566,7 +566,7 @@ theorem mk_eq_mk_of_basis (v : Basis ι R M) (v' : Basis ι' R M) :
 #align mk_eq_mk_of_basis mk_eq_mk_of_basis
 
 /-- Given two bases indexed by `ι` and `ι'` of an `R`-module, where `R` satisfies the invariant
-basis number property, an equiv `ι ≃ ι' `. -/
+basis number property, an equiv `ι ≃ ι'`. -/
 def Basis.indexEquiv (v : Basis ι R M) (v' : Basis ι' R M) : ι ≃ ι' :=
   (Cardinal.lift_mk_eq'.1 <| mk_eq_mk_of_basis v v').some
 #align basis.index_equiv Basis.indexEquiv

These carry no data so should be harmless.

@@ -1013,6 +1013,10 @@ theorem rank_prod : Module.rank K (V × V') =
 theorem rank_prod' : Module.rank K (V × V₁) = Module.rank K V + Module.rank K V₁ := by simp
 #align rank_prod' rank_prod'
 
+@[simp]
+theorem rank_ulift : Module.rank K (ULift.{w} V) = Cardinal.lift.{w} (Module.rank K V) :=
+  Cardinal.lift_injective.{v} <| Eq.symm <| (lift_lift _).trans ULift.moduleEquiv.symm.lift_rank_eq
+
 section Fintype
 
 variable [∀ i, AddCommGroup (φ i)] [∀ i, Module K (φ i)] [∀ i, Module.Free K (φ i)]

@@ -1118,7 +1118,7 @@ theorem rank_eq_of_surjective (f : V →ₗ[K] V₁) (h : Surjective f) :
 
 /-- Given a family of `n` linearly independent vectors in a space of dimension `> n`, one may extend
 the family by another vector while retaining linear independence. -/
-theorem exists_linear_independent_cons_of_lt_rank {n : ℕ} {v : Fin n → V}
+theorem exists_linearIndependent_cons_of_lt_rank {n : ℕ} {v : Fin n → V}
     (hv : LinearIndependent K v) (h : n < Module.rank K V) :
     ∃ (x : V), LinearIndependent K (Fin.cons x v) := by
   have A : Submodule.span K (range v) ≠ ⊤ := by
@@ -1136,18 +1136,18 @@ theorem exists_linear_independent_cons_of_lt_rank {n : ℕ} {v : Fin n → V}
 
 /-- Given a family of `n` linearly independent vectors in a space of dimension `> n`, one may extend
 the family by another vector while retaining linear independence. -/
-theorem exists_linear_independent_snoc_of_lt_rank {n : ℕ} {v : Fin n → V}
+theorem exists_linearIndependent_snoc_of_lt_rank {n : ℕ} {v : Fin n → V}
     (hv : LinearIndependent K v) (h : n < Module.rank K V) :
     ∃ (x : V), LinearIndependent K (Fin.snoc v x) := by
   simpa [linearIndependent_fin_cons, ← linearIndependent_fin_snoc]
-    using exists_linear_independent_cons_of_lt_rank hv h
+    using exists_linearIndependent_cons_of_lt_rank hv h
 
 /-- Given a nonzero vector in a space of dimension `> 1`, one may find another vector linearly
 independent of the first one. -/
-theorem exists_linear_independent_pair_of_one_lt_rank
+theorem exists_linearIndependent_pair_of_one_lt_rank
     (h : 1 < Module.rank K V) {x : V} (hx : x ≠ 0) :
     ∃ y, LinearIndependent K ![x, y] := by
-  obtain ⟨y, hy⟩ := exists_linear_independent_snoc_of_lt_rank (linearIndependent_unique ![x] hx) h
+  obtain ⟨y, hy⟩ := exists_linearIndependent_snoc_of_lt_rank (linearIndependent_unique ![x] hx) h
   have : Fin.snoc ![x] y = ![x, y] := Iff.mp List.ofFn_inj rfl
   rw [this] at hy
   exact ⟨y, hy⟩

This adds a trivial cardinality argument that shows that when V is a free K-module where K is infinite and satisfies the strong rank condiiton, then the rank of V coincides with its cardinality. This is then used to establish that Module.rank ℚ ℝ = continuum = Module.rank ℚ ℂ, and therefore that ℝ and ℂ are isomorphic as vector spaces over ℚ.

As requested on Zulip

@@ -935,6 +935,17 @@ theorem rank_eq_card_chooseBasisIndex : Module.rank K V = #(ChooseBasisIndex K V
   (chooseBasis K V).mk_eq_rank''.symm
 #align module.free.rank_eq_card_choose_basis_index Module.Free.rank_eq_card_chooseBasisIndex
 
+/-- The rank of a free module `V` over an infinite scalar ring `K` is the cardinality of `V`
+whenever `#R < #V`. -/
+lemma rank_eq_mk_of_infinite_lt [Infinite K] (h_lt : lift.{v} #K < lift.{u} #V) :
+    Module.rank K V = #V := by
+  have : Infinite V := infinite_iff.mpr <| lift_le.mp <| le_trans (by simp) h_lt.le
+  have h : lift #V = lift #(ChooseBasisIndex K V →₀ K) := lift_mk_eq'.mpr ⟨(chooseBasis K V).repr⟩
+  simp only [mk_finsupp_lift_of_infinite', lift_id', ← rank_eq_card_chooseBasisIndex, lift_max,
+    lift_lift] at h
+  refine lift_inj.mp ((max_eq_iff.mp h.symm).resolve_right <| not_and_of_not_left _ ?_).left
+  exact (lift_umax.{v, u}.symm ▸ h_lt).ne
+
 end Module.Free
 
 open Module.Free

@@ -1105,6 +1105,42 @@ theorem rank_eq_of_surjective (f : V →ₗ[K] V₁) (h : Surjective f) :
   rw [← rank_range_add_rank_ker f, ← rank_range_of_surjective f h]
 #align rank_eq_of_surjective rank_eq_of_surjective
 
+/-- Given a family of `n` linearly independent vectors in a space of dimension `> n`, one may extend
+the family by another vector while retaining linear independence. -/
+theorem exists_linear_independent_cons_of_lt_rank {n : ℕ} {v : Fin n → V}
+    (hv : LinearIndependent K v) (h : n < Module.rank K V) :
+    ∃ (x : V), LinearIndependent K (Fin.cons x v) := by
+  have A : Submodule.span K (range v) ≠ ⊤ := by
+    intro H
+    rw [← rank_top, ← H] at h
+    have : Module.rank K (Submodule.span K (range v)) ≤ n := by
+      have := Cardinal.mk_range_le_lift (f := v)
+      simp only [Cardinal.lift_id'] at this
+      exact (rank_span_le _).trans (this.trans (by simp))
+    exact lt_irrefl _ (h.trans_le this)
+  obtain ⟨x, hx⟩ : ∃ x, x ∉ Submodule.span K (range v) := by
+    contrapose! A
+    exact Iff.mpr Submodule.eq_top_iff' A
+  exact ⟨x, linearIndependent_fin_cons.2 ⟨hv, hx⟩⟩
+
+/-- Given a family of `n` linearly independent vectors in a space of dimension `> n`, one may extend
+the family by another vector while retaining linear independence. -/
+theorem exists_linear_independent_snoc_of_lt_rank {n : ℕ} {v : Fin n → V}
+    (hv : LinearIndependent K v) (h : n < Module.rank K V) :
+    ∃ (x : V), LinearIndependent K (Fin.snoc v x) := by
+  simpa [linearIndependent_fin_cons, ← linearIndependent_fin_snoc]
+    using exists_linear_independent_cons_of_lt_rank hv h
+
+/-- Given a nonzero vector in a space of dimension `> 1`, one may find another vector linearly
+independent of the first one. -/
+theorem exists_linear_independent_pair_of_one_lt_rank
+    (h : 1 < Module.rank K V) {x : V} (hx : x ≠ 0) :
+    ∃ y, LinearIndependent K ![x, y] := by
+  obtain ⟨y, hy⟩ := exists_linear_independent_snoc_of_lt_rank (linearIndependent_unique ![x] hx) h
+  have : Fin.snoc ![x] y = ![x, y] := Iff.mp List.ofFn_inj rfl
+  rw [this] at hy
+  exact ⟨y, hy⟩
+
 section
 
 variable [AddCommGroup V₂] [Module K V₂]

Previously, a statement like:

import Mathlib.LinearAlgebra.Dimension
import Mathlib.Tactic

variable {K : Type} [Field K]
variable {V W : Type} [AddCommGroup V] [AddCommGroup W] [Module K V] [Module K W]
variable {L : V →ₗ[K] W}

open LinearMap (ker)
open Module (rank)

example : rank K V = L.rank + rank K (ker L) := by
    sorry

required rewriting LinearMap.rank before manually finding the existence of rank_range_add_rank_ker.

After this change though, exact? successfully finds the lemma / solves the above.

@@ -1318,7 +1318,7 @@ variable [Ring K] [AddCommGroup V] [Module K V] [AddCommGroup V₁] [Module K V
 variable [AddCommGroup V'] [Module K V']
 
 /-- `rank f` is the rank of a `LinearMap` `f`, defined as the dimension of `f.range`. -/
-def rank (f : V →ₗ[K] V') : Cardinal :=
+abbrev rank (f : V →ₗ[K] V') : Cardinal :=
   Module.rank K (LinearMap.range f)
 #align linear_map.rank LinearMap.rank
 

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

This has nice performance benefits.

@@ -80,7 +80,7 @@ universe u v v' v'' u₁' w w'
 
 variable {K : Type u} {V V₁ V₂ V₃ : Type v} {V' V'₁ : Type v'} {V'' : Type v''}
 
-variable {ι : Type w} {ι' : Type w'} {η : Type u₁'} {φ : η → Type _}
+variable {ι : Type w} {ι' : Type w'} {η : Type u₁'} {φ : η → Type*}
 
 open BigOperators Cardinal Basis Submodule Function Set
 
@@ -590,7 +590,7 @@ then for any finite basis `b : Basis ι R M`,
 and any finite spanning set `w : Set M`,
 the cardinality of `ι` is bounded by the cardinality of `w`.
 -/
-theorem Basis.le_span'' {ι : Type _} [Fintype ι] (b : Basis ι R M) {w : Set M} [Fintype w]
+theorem Basis.le_span'' {ι : Type*} [Fintype ι] (b : Basis ι R M) {w : Set M} [Fintype w]
     (s : span R w = ⊤) : Fintype.card ι ≤ Fintype.card w := by
   -- We construct a surjective linear map `(w → R) →ₗ[R] (ι → R)`,
   -- by expressing a linear combination in `w` as a linear combination in `ι`.
@@ -606,7 +606,7 @@ theorem Basis.le_span'' {ι : Type _} [Fintype ι] (b : Basis ι R M) {w : Set M
 Another auxiliary lemma for `Basis.le_span`, which does not require assuming the basis is finite,
 but still assumes we have a finite spanning set.
 -/
-theorem basis_le_span' {ι : Type _} (b : Basis ι R M) {w : Set M} [Fintype w] (s : span R w = ⊤) :
+theorem basis_le_span' {ι : Type*} (b : Basis ι R M) {w : Set M} [Fintype w] (s : span R w = ⊤) :
     #ι ≤ Fintype.card w := by
   haveI := nontrivial_of_invariantBasisNumber R
   haveI := basis_finite_of_finite_spans w (toFinite _) s b
@@ -660,7 +660,7 @@ open Submodule
 
 -- An auxiliary lemma for `linearIndependent_le_span'`,
 -- with the additional assumption that the linearly independent family is finite.
-theorem linearIndependent_le_span_aux' {ι : Type _} [Fintype ι] (v : ι → M)
+theorem linearIndependent_le_span_aux' {ι : Type*} [Fintype ι] (v : ι → M)
     (i : LinearIndependent R v) (w : Set M) [Fintype w] (s : range v ≤ span R w) :
     Fintype.card ι ≤ Fintype.card w := by
   -- We construct an injective linear map `(ι → R) →ₗ[R] (w → R)`,
@@ -682,7 +682,7 @@ then any linearly independent family `v : ι → M`
 contained in the span of some finite `w : Set M`,
 is itself finite.
 -/
-def linearIndependentFintypeOfLeSpanFintype {ι : Type _} (v : ι → M) (i : LinearIndependent R v)
+def linearIndependentFintypeOfLeSpanFintype {ι : Type*} (v : ι → M) (i : LinearIndependent R v)
     (w : Set M) [Fintype w] (s : range v ≤ span R w) : Fintype ι :=
   fintypeOfFinsetCardLe (Fintype.card w) fun t => by
     let v' := fun x : (t : Set ι) => v x
@@ -696,7 +696,7 @@ then for any linearly independent family `v : ι → M`
 contained in the span of some finite `w : Set M`,
 the cardinality of `ι` is bounded by the cardinality of `w`.
 -/
-theorem linearIndependent_le_span' {ι : Type _} (v : ι → M) (i : LinearIndependent R v) (w : Set M)
+theorem linearIndependent_le_span' {ι : Type*} (v : ι → M) (i : LinearIndependent R v) (w : Set M)
     [Fintype w] (s : range v ≤ span R w) : #ι ≤ Fintype.card w := by
   haveI : Fintype ι := linearIndependentFintypeOfLeSpanFintype v i w s
   rw [Cardinal.mk_fintype]
@@ -709,7 +709,7 @@ then for any linearly independent family `v : ι → M`
 and any finite spanning set `w : Set M`,
 the cardinality of `ι` is bounded by the cardinality of `w`.
 -/
-theorem linearIndependent_le_span {ι : Type _} (v : ι → M) (i : LinearIndependent R v) (w : Set M)
+theorem linearIndependent_le_span {ι : Type*} (v : ι → M) (i : LinearIndependent R v) (w : Set M)
     [Fintype w] (s : span R w = ⊤) : #ι ≤ Fintype.card w := by
   apply linearIndependent_le_span' v i w
   rw [s]
@@ -717,7 +717,7 @@ theorem linearIndependent_le_span {ι : Type _} (v : ι → M) (i : LinearIndepe
 #align linear_independent_le_span linearIndependent_le_span
 
 /-- A version of `linearIndependent_le_span` for `Finset`. -/
-theorem linearIndependent_le_span_finset {ι : Type _} (v : ι → M) (i : LinearIndependent R v)
+theorem linearIndependent_le_span_finset {ι : Type*} (v : ι → M) (i : LinearIndependent R v)
     (w : Finset M) (s : span R (w : Set M) = ⊤) : #ι ≤ w.card := by
   simpa only [Finset.coe_sort_coe, Fintype.card_coe] using linearIndependent_le_span v i w s
 #align linear_independent_le_span_finset linearIndependent_le_span_finset
@@ -725,7 +725,7 @@ theorem linearIndependent_le_span_finset {ι : Type _} (v : ι → M) (i : Linea
 /-- An auxiliary lemma for `linearIndependent_le_basis`:
 we handle the case where the basis `b` is infinite.
 -/
-theorem linearIndependent_le_infinite_basis {ι : Type _} (b : Basis ι R M) [Infinite ι] {κ : Type _}
+theorem linearIndependent_le_infinite_basis {ι : Type*} (b : Basis ι R M) [Infinite ι] {κ : Type _}
     (v : κ → M) (i : LinearIndependent R v) : #κ ≤ #ι := by
   classical
   by_contra h
@@ -747,7 +747,7 @@ if `b` is a basis for a module `M`,
 and `s` is a linearly independent set,
 then the cardinality of `s` is bounded by the cardinality of `b`.
 -/
-theorem linearIndependent_le_basis {ι : Type _} (b : Basis ι R M) {κ : Type _} (v : κ → M)
+theorem linearIndependent_le_basis {ι : Type*} (b : Basis ι R M) {κ : Type _} (v : κ → M)
     (i : LinearIndependent R v) : #κ ≤ #ι := by
   classical
   -- We split into cases depending on whether `ι` is infinite.
@@ -762,7 +762,7 @@ theorem linearIndependent_le_basis {ι : Type _} (b : Basis ι R M) {κ : Type _
 
 /-- Let `R` satisfy the strong rank condition. If `m` elements of a free rank `n` `R`-module are
 linearly independent, then `m ≤ n`. -/
-theorem Basis.card_le_card_of_linearIndependent_aux {R : Type _} [Ring R] [StrongRankCondition R]
+theorem Basis.card_le_card_of_linearIndependent_aux {R : Type*} [Ring R] [StrongRankCondition R]
     (n : ℕ) {m : ℕ} (v : Fin m → Fin n → R) : LinearIndependent R v → m ≤ n := fun h => by
   simpa using linearIndependent_le_basis (Pi.basisFun R (Fin n)) v h
 #align basis.card_le_card_of_linear_independent_aux Basis.card_le_card_of_linearIndependent_aux
@@ -775,7 +775,7 @@ then every maximal linearly independent set has the same cardinality as `b`.
 This proof (along with some of the lemmas above) comes from
 [Les familles libres maximales d'un module ont-elles le meme cardinal?][lazarus1973]
 -/
-theorem maximal_linearIndependent_eq_infinite_basis {ι : Type _} (b : Basis ι R M) [Infinite ι]
+theorem maximal_linearIndependent_eq_infinite_basis {ι : Type*} (b : Basis ι R M) [Infinite ι]
     {κ : Type _} (v : κ → M) (i : LinearIndependent R v) (m : i.Maximal) : #κ = #ι := by
   apply le_antisymm
   · exact linearIndependent_le_basis b v i
@@ -814,8 +814,8 @@ theorem rank_eq_card_basis {ι : Type w} [Fintype ι] (h : Basis ι R M) :
   rw [← h.mk_range_eq_rank, Cardinal.mk_fintype, Set.card_range_of_injective h.injective]
 #align rank_eq_card_basis rank_eq_card_basis
 
-theorem Basis.card_le_card_of_linearIndependent {ι : Type _} [Fintype ι] (b : Basis ι R M)
-    {ι' : Type _} [Fintype ι'] {v : ι' → M} (hv : LinearIndependent R v) :
+theorem Basis.card_le_card_of_linearIndependent {ι : Type*} [Fintype ι] (b : Basis ι R M)
+    {ι' : Type*} [Fintype ι'] {v : ι' → M} (hv : LinearIndependent R v) :
     Fintype.card ι' ≤ Fintype.card ι := by
   letI := nontrivial_of_invariantBasisNumber R
   simpa [rank_eq_card_basis b, Cardinal.mk_fintype] using
@@ -845,20 +845,20 @@ theorem Basis.mk_eq_rank'.{m} (v : Basis ι R M) :
 #align basis.mk_eq_rank' Basis.mk_eq_rank'
 
 /-- If a module has a finite dimension, all bases are indexed by a finite type. -/
-theorem Basis.nonempty_fintype_index_of_rank_lt_aleph0 {ι : Type _} (b : Basis ι R M)
+theorem Basis.nonempty_fintype_index_of_rank_lt_aleph0 {ι : Type*} (b : Basis ι R M)
     (h : Module.rank R M < ℵ₀) : Nonempty (Fintype ι) := by
   rwa [← Cardinal.lift_lt, ← b.mk_eq_rank, Cardinal.lift_aleph0, Cardinal.lift_lt_aleph0,
     Cardinal.lt_aleph0_iff_fintype] at h
 #align basis.nonempty_fintype_index_of_rank_lt_aleph_0 Basis.nonempty_fintype_index_of_rank_lt_aleph0
 
 /-- If a module has a finite dimension, all bases are indexed by a finite type. -/
-noncomputable def Basis.fintypeIndexOfRankLtAleph0 {ι : Type _} (b : Basis ι R M)
+noncomputable def Basis.fintypeIndexOfRankLtAleph0 {ι : Type*} (b : Basis ι R M)
     (h : Module.rank R M < ℵ₀) : Fintype ι :=
   Classical.choice (b.nonempty_fintype_index_of_rank_lt_aleph0 h)
 #align basis.fintype_index_of_rank_lt_aleph_0 Basis.fintypeIndexOfRankLtAleph0
 
 /-- If a module has a finite dimension, all bases are indexed by a finite set. -/
-theorem Basis.finite_index_of_rank_lt_aleph0 {ι : Type _} {s : Set ι} (b : Basis s R M)
+theorem Basis.finite_index_of_rank_lt_aleph0 {ι : Type*} {s : Set ι} (b : Basis s R M)
     (h : Module.rank R M < ℵ₀) : s.Finite :=
   finite_def.2 (b.nonempty_fintype_index_of_rank_lt_aleph0 h)
 #align basis.finite_index_of_rank_lt_aleph_0 Basis.finite_index_of_rank_lt_aleph0
@@ -881,7 +881,7 @@ finite free module `M`. A property is true for all submodules of `M` if it satis
 "inductive step": the property is true for a submodule `N` if it's true for all submodules `N'`
 of `N` with the property that there exists `0 ≠ x ∈ N` such that the sum `N' + Rx` is direct. -/
 def Submodule.inductionOnRank [IsDomain R] [Fintype ι] (b : Basis ι R M)
-    (P : Submodule R M → Sort _) (ih : ∀ N : Submodule R M,
+    (P : Submodule R M → Sort*) (ih : ∀ N : Submodule R M,
     (∀ N' ≤ N, ∀ x ∈ N, (∀ (c : R), ∀ y ∈ N', c • x + y = (0 : M) → c = 0) → P N') → P N)
     (N : Submodule R M) : P N :=
   Submodule.inductionOnRankAux b P ih (Fintype.card ι) N fun hs hli => by
@@ -890,8 +890,8 @@ def Submodule.inductionOnRank [IsDomain R] [Fintype ι] (b : Basis ι R M)
 
 /-- If `S` a module-finite free `R`-algebra, then the `R`-rank of a nonzero `R`-free
 ideal `I` of `S` is the same as the rank of `S`. -/
-theorem Ideal.rank_eq {R S : Type _} [CommRing R] [StrongRankCondition R] [Ring S] [IsDomain S]
-    [Algebra R S] {n m : Type _} [Fintype n] [Fintype m] (b : Basis n R S) {I : Ideal S}
+theorem Ideal.rank_eq {R S : Type*} [CommRing R] [StrongRankCondition R] [Ring S] [IsDomain S]
+    [Algebra R S] {n m : Type*} [Fintype n] [Fintype m] (b : Basis n R S) {I : Ideal S}
     (hI : I ≠ ⊥) (c : Basis m R I) : Fintype.card m = Fintype.card n := by
   obtain ⟨a, ha⟩ := Submodule.nonzero_mem_of_bot_lt (bot_lt_iff_ne_bot.mpr hI)
   have : LinearIndependent R fun i => b i • a := by
@@ -1179,13 +1179,13 @@ variable [AddCommGroup V'] [Module K V']
 
 See also `FiniteDimensional.finBasis`.
 -/
-def Basis.ofRankEqZero {ι : Type _} [IsEmpty ι] (hV : Module.rank K V = 0) : Basis ι K V :=
+def Basis.ofRankEqZero {ι : Type*} [IsEmpty ι] (hV : Module.rank K V = 0) : Basis ι K V :=
   haveI : Subsingleton V := rank_zero_iff.1 hV
   Basis.empty _
 #align basis.of_rank_eq_zero Basis.ofRankEqZero
 
 @[simp]
-theorem Basis.ofRankEqZero_apply {ι : Type _} [IsEmpty ι] (hV : Module.rank K V = 0) (i : ι) :
+theorem Basis.ofRankEqZero_apply {ι : Type*} [IsEmpty ι] (hV : Module.rank K V = 0) (i : ι) :
     Basis.ofRankEqZero hV i = 0 :=
   rfl
 #align basis.of_rank_eq_zero_apply Basis.ofRankEqZero_apply

This also changes basisFintypeOfFiniteSpans to use Finite rather than Fintype, as it was noncomputable anyway. This means it has to be renamed to basis_finite_of_finite_spans as it now is a proof!

Co-authored-by: Oliver Nash <github@olivernash.org>

@@ -30,7 +30,7 @@ import Mathlib.SetTheory.Cardinal.Cofinality
   at most that of the target.
 * `LinearMap.rank_le_of_surjective`: the target of a surjective linear map has dimension
   at most that of that source.
-* `basisFintypeOfFiniteSpans`:
+* `basis_finite_of_finite_spans`:
   the existence of a finite spanning set implies that any basis is finite.
 * `infinite_basis_le_maximal_linearIndependent`:
   if `b` is an infinite basis for a module `M`,
@@ -319,11 +319,13 @@ theorem LinearIndependent.set_finite_of_isNoetherian [IsNoetherian R M] {s : Set
 /--
 Over any nontrivial ring, the existence of a finite spanning set implies that any basis is finite.
 -/
-def basisFintypeOfFiniteSpans (w : Set M) [Fintype w] (s : span R w = ⊤) {ι : Type w}
-    (b : Basis ι R M) : Fintype ι := by
+lemma basis_finite_of_finite_spans (w : Set M) (hw : w.Finite) (s : span R w = ⊤) {ι : Type w}
+    (b : Basis ι R M) : Finite ι := by
   classical
+  haveI := hw.to_subtype
+  cases nonempty_fintype w
   -- We'll work by contradiction, assuming `ι` is infinite.
-  apply fintypeOfNotInfinite _
+  rw [← not_infinite_iff_finite]
   intro i
   -- Let `S` be the union of the supports of `x ∈ w` expressed as linear combinations of `b`.
   -- This is a finite set since `w` is finite.
@@ -348,7 +350,7 @@ def basisFintypeOfFiniteSpans (w : Set M) [Fintype w] (s : span R w = ⊤) {ι :
   -- giving the desire contradiction.
   refine' b.linearIndependent.not_mem_span_image _ k'
   exact nm
-#align basis_fintype_of_finite_spans basisFintypeOfFiniteSpans
+#align basis_fintype_of_finite_spans basis_finite_of_finite_spansₓ
 
 -- From [Les familles libres maximales d'un module ont-elles le meme cardinal?][lazarus1973]
 /-- Over any ring `R`, if `b` is a basis for a module `M`,
@@ -540,9 +542,10 @@ theorem mk_eq_mk_of_basis (v : Basis ι R M) (v' : Basis ι' R M) :
   classical
   haveI := nontrivial_of_invariantBasisNumber R
   cases fintypeOrInfinite ι
-  · -- `v` is a finite basis, so by `basisFintypeOfFiniteSpans` so is `v'`.
-    haveI : Fintype (range v) := Set.fintypeRange v
-    haveI := basisFintypeOfFiniteSpans _ v.span_eq v'
+  · -- `v` is a finite basis, so by `basis_finite_of_finite_spans` so is `v'`.
+    -- haveI : Finite (range v) := Set.finite_range v
+    haveI := basis_finite_of_finite_spans _ (Set.finite_range v) v.span_eq v'
+    cases nonempty_fintype ι'
     -- We clean up a little:
     rw [Cardinal.mk_fintype, Cardinal.mk_fintype]
     simp only [Cardinal.lift_natCast, Cardinal.natCast_inj]
@@ -606,7 +609,8 @@ but still assumes we have a finite spanning set.
 theorem basis_le_span' {ι : Type _} (b : Basis ι R M) {w : Set M} [Fintype w] (s : span R w = ⊤) :
     #ι ≤ Fintype.card w := by
   haveI := nontrivial_of_invariantBasisNumber R
-  haveI := basisFintypeOfFiniteSpans w s b
+  haveI := basis_finite_of_finite_spans w (toFinite _) s b
+  cases nonempty_fintype ι
   rw [Cardinal.mk_fintype ι]
   simp only [Cardinal.natCast_le]
   exact Basis.le_span'' b s

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.

@@ -82,7 +82,7 @@ variable {K : Type u} {V V₁ V₂ V₃ : Type v} {V' V'₁ : Type v'} {V'' : Ty
 
 variable {ι : Type w} {ι' : Type w'} {η : Type u₁'} {φ : η → Type _}
 
-open Classical BigOperators Cardinal Basis Submodule Function Set
+open BigOperators Cardinal Basis Submodule Function Set
 
 section Module
 
@@ -321,6 +321,7 @@ Over any nontrivial ring, the existence of a finite spanning set implies that an
 -/
 def basisFintypeOfFiniteSpans (w : Set M) [Fintype w] (s : span R w = ⊤) {ι : Type w}
     (b : Basis ι R M) : Fintype ι := by
+  classical
   -- We'll work by contradiction, assuming `ι` is infinite.
   apply fintypeOfNotInfinite _
   intro i
@@ -536,6 +537,7 @@ variable {M : Type v} [AddCommGroup M] [Module R M]
 have the same cardinalities. -/
 theorem mk_eq_mk_of_basis (v : Basis ι R M) (v' : Basis ι' R M) :
     Cardinal.lift.{w'} #ι = Cardinal.lift.{w} #ι' := by
+  classical
   haveI := nontrivial_of_invariantBasisNumber R
   cases fintypeOrInfinite ι
   · -- `v` is a finite basis, so by `basisFintypeOfFiniteSpans` so is `v'`.
@@ -721,6 +723,7 @@ we handle the case where the basis `b` is infinite.
 -/
 theorem linearIndependent_le_infinite_basis {ι : Type _} (b : Basis ι R M) [Infinite ι] {κ : Type _}
     (v : κ → M) (i : LinearIndependent R v) : #κ ≤ #ι := by
+  classical
   by_contra h
   rw [not_le, ← Cardinal.mk_finset_of_infinite ι] at h
   let Φ := fun k : κ => (b.repr (v k)).support
@@ -742,6 +745,7 @@ then the cardinality of `s` is bounded by the cardinality of `b`.
 -/
 theorem linearIndependent_le_basis {ι : Type _} (b : Basis ι R M) {κ : Type _} (v : κ → M)
     (i : LinearIndependent R v) : #κ ≤ #ι := by
+  classical
   -- We split into cases depending on whether `ι` is infinite.
   cases fintypeOrInfinite ι
   · rw [Cardinal.mk_fintype ι] -- When `ι` is finite, we have `linearIndependent_le_span`,
@@ -801,6 +805,7 @@ theorem Basis.mk_range_eq_rank (v : Basis ι R M) : #(range v) = Module.rank R M
 cardinality of the basis. -/
 theorem rank_eq_card_basis {ι : Type w} [Fintype ι] (h : Basis ι R M) :
     Module.rank R M = Fintype.card ι := by
+  classical
   haveI := nontrivial_of_invariantBasisNumber R
   rw [← h.mk_range_eq_rank, Cardinal.mk_fintype, Set.card_range_of_injective h.injective]
 #align rank_eq_card_basis rank_eq_card_basis

This breaks a dependency cycle with Module.Free, which means we can immediately show that all vector spaces are free modules.

The lemmas are moved without modification in this PR. A subsequent PR can use the Module.Free results to golf the vector space ones, and deduplicate the API.

Co-authored-by: Oliver Nash <github@olivernash.org>

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 -/
 import Mathlib.Algebra.Module.BigOperators
+import Mathlib.LinearAlgebra.Basis.VectorSpace
 import Mathlib.LinearAlgebra.DFinsupp
 import Mathlib.LinearAlgebra.FreeModule.Basic
 import Mathlib.LinearAlgebra.InvariantBasisNumber

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

@@ -198,10 +198,10 @@ theorem LinearEquiv.rank_eq (f : M ≃ₗ[R] M₁) : Module.rank R M = Module.ra
   Cardinal.lift_inj.1 f.lift_rank_eq
 #align linear_equiv.rank_eq LinearEquiv.rank_eq
 
-theorem rank_eq_of_injective (f : M →ₗ[R] M₁) (h : Injective f) :
-    Module.rank R M = Module.rank R (LinearMap.range f) :=
-  (LinearEquiv.ofInjective f h).rank_eq
-#align rank_eq_of_injective rank_eq_of_injective
+theorem rank_range_of_injective (f : M →ₗ[R] M₁) (h : Injective f) :
+    Module.rank R (LinearMap.range f) = Module.rank R M :=
+  (LinearEquiv.ofInjective f h).rank_eq.symm
+#align rank_eq_of_injective rank_range_of_injective
 
 /-- Pushforwards of submodules along a `LinearEquiv` have the same dimension. -/
 theorem LinearEquiv.rank_map_eq (f : M ≃ₗ[R] M₁) (p : Submodule R M) :

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2018 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
-
-! This file was ported from Lean 3 source module linear_algebra.dimension
-! leanprover-community/mathlib commit 47a5f8186becdbc826190ced4312f8199f9db6a5
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Module.BigOperators
 import Mathlib.LinearAlgebra.DFinsupp
@@ -16,6 +11,8 @@ import Mathlib.LinearAlgebra.Isomorphisms
 import Mathlib.LinearAlgebra.StdBasis
 import Mathlib.SetTheory.Cardinal.Cofinality
 
+#align_import linear_algebra.dimension from "leanprover-community/mathlib"@"47a5f8186becdbc826190ced4312f8199f9db6a5"
+
 /-!
 # Dimension of modules and vector spaces
 

See #4354

@@ -9,7 +9,7 @@ Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 ! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Module.BigOperators
-import Mathlib.LinearAlgebra.Dfinsupp
+import Mathlib.LinearAlgebra.DFinsupp
 import Mathlib.LinearAlgebra.FreeModule.Basic
 import Mathlib.LinearAlgebra.InvariantBasisNumber
 import Mathlib.LinearAlgebra.Isomorphisms

@@ -246,7 +246,7 @@ variable [Nontrivial R]
 
 theorem cardinal_lift_le_rank_of_linearIndependent {ι : Type w} {v : ι → M}
     (hv : LinearIndependent R v) :
-    Cardinal.lift.{v} (#ι) ≤ Cardinal.lift.{w} (Module.rank R M) := by
+    Cardinal.lift.{v} #ι ≤ Cardinal.lift.{w} (Module.rank R M) := by
   apply le_trans
   · exact Cardinal.lift_mk_le'.mpr ⟨(Equiv.ofInjective _ hv.injective).toEmbedding⟩
   · simp only [Cardinal.lift_le, Module.rank_def]
@@ -257,17 +257,17 @@ theorem cardinal_lift_le_rank_of_linearIndependent {ι : Type w} {v : ι → M}
 #align cardinal_lift_le_rank_of_linear_independent cardinal_lift_le_rank_of_linearIndependent
 
 theorem cardinal_lift_le_rank_of_linearIndependent' {ι : Type w} {v : ι → M}
-    (hv : LinearIndependent R v) : Cardinal.lift.{v} (#ι) ≤ Cardinal.lift.{w} (Module.rank R M) :=
+    (hv : LinearIndependent R v) : Cardinal.lift.{v} #ι ≤ Cardinal.lift.{w} (Module.rank R M) :=
   cardinal_lift_le_rank_of_linearIndependent hv
 #align cardinal_lift_le_rank_of_linear_independent' cardinal_lift_le_rank_of_linearIndependent'
 
 theorem cardinal_le_rank_of_linearIndependent {ι : Type v} {v : ι → M}
-    (hv : LinearIndependent R v) : (#ι) ≤ Module.rank R M := by
+    (hv : LinearIndependent R v) : #ι ≤ Module.rank R M := by
   simpa using cardinal_lift_le_rank_of_linearIndependent hv
 #align cardinal_le_rank_of_linear_independent cardinal_le_rank_of_linearIndependent
 
 theorem cardinal_le_rank_of_linearIndependent' {s : Set M}
-    (hs : LinearIndependent R (fun x => x : s → M)) : (#s) ≤ Module.rank R M :=
+    (hs : LinearIndependent R (fun x => x : s → M)) : #s ≤ Module.rank R M :=
   cardinal_le_rank_of_linearIndependent hs
 #align cardinal_le_rank_of_linear_independent' cardinal_le_rank_of_linearIndependent'
 
@@ -429,12 +429,12 @@ then the cardinality of `b` is bounded by the cardinality of `s`.
 -/
 theorem infinite_basis_le_maximal_linearIndependent' {ι : Type w} (b : Basis ι R M) [Infinite ι]
     {κ : Type w'} (v : κ → M) (i : LinearIndependent R v) (m : i.Maximal) :
-    Cardinal.lift.{w'} (#ι) ≤ Cardinal.lift.{w} (#κ) := by
+    Cardinal.lift.{w'} #ι ≤ Cardinal.lift.{w} #κ := by
   let Φ := fun k : κ => (b.repr (v k)).support
-  have w₁ : (#ι) ≤ (#Set.range Φ) := by
+  have w₁ : #ι ≤ #(Set.range Φ) := by
     apply Cardinal.le_range_of_union_finset_eq_top
     exact union_support_maximal_linearIndependent_eq_range_basis b v i m
-  have w₂ : Cardinal.lift.{w'} (#Set.range Φ) ≤ Cardinal.lift.{w} (#κ) := Cardinal.mk_range_le_lift
+  have w₂ : Cardinal.lift.{w'} #(Set.range Φ) ≤ Cardinal.lift.{w} #κ := Cardinal.mk_range_le_lift
   exact (Cardinal.lift_le.mpr w₁).trans w₂
 #align infinite_basis_le_maximal_linear_independent' infinite_basis_le_maximal_linearIndependent'
 
@@ -445,13 +445,13 @@ and `s` is a maximal linearly independent set,
 then the cardinality of `b` is bounded by the cardinality of `s`.
 -/
 theorem infinite_basis_le_maximal_linearIndependent {ι : Type w} (b : Basis ι R M) [Infinite ι]
-    {κ : Type w} (v : κ → M) (i : LinearIndependent R v) (m : i.Maximal) : (#ι) ≤ (#κ) :=
+    {κ : Type w} (v : κ → M) (i : LinearIndependent R v) (m : i.Maximal) : #ι ≤ #κ :=
   Cardinal.lift_le.mp (infinite_basis_le_maximal_linearIndependent' b v i m)
 #align infinite_basis_le_maximal_linear_independent infinite_basis_le_maximal_linearIndependent
 
 theorem CompleteLattice.Independent.subtype_ne_bot_le_rank [NoZeroSMulDivisors R M]
     {V : ι → Submodule R M} (hV : CompleteLattice.Independent V) :
-    Cardinal.lift.{v} (#{ i : ι // V i ≠ ⊥ }) ≤ Cardinal.lift.{w} (Module.rank R M) := by
+    Cardinal.lift.{v} #{ i : ι // V i ≠ ⊥ } ≤ Cardinal.lift.{w} (Module.rank R M) := by
   set I := { i : ι // V i ≠ ⊥ }
   have hI : ∀ i : I, ∃ v ∈ V i, v ≠ (0 : M) := by
     intro i
@@ -537,7 +537,7 @@ variable {M : Type v} [AddCommGroup M] [Module R M]
 /-- The dimension theorem: if `v` and `v'` are two bases, their index types
 have the same cardinalities. -/
 theorem mk_eq_mk_of_basis (v : Basis ι R M) (v' : Basis ι' R M) :
-    Cardinal.lift.{w'} (#ι) = Cardinal.lift.{w} (#ι') := by
+    Cardinal.lift.{w'} #ι = Cardinal.lift.{w} #ι' := by
   haveI := nontrivial_of_invariantBasisNumber R
   cases fintypeOrInfinite ι
   · -- `v` is a finite basis, so by `basisFintypeOfFiniteSpans` so is `v'`.
@@ -568,7 +568,7 @@ def Basis.indexEquiv (v : Basis ι R M) (v' : Basis ι' R M) : ι ≃ ι' :=
   (Cardinal.lift_mk_eq'.1 <| mk_eq_mk_of_basis v v').some
 #align basis.index_equiv Basis.indexEquiv
 
-theorem mk_eq_mk_of_basis' {ι' : Type w} (v : Basis ι R M) (v' : Basis ι' R M) : (#ι) = (#ι') :=
+theorem mk_eq_mk_of_basis' {ι' : Type w} (v : Basis ι R M) (v' : Basis ι' R M) : #ι = #ι' :=
   Cardinal.lift_inj.1 <| mk_eq_mk_of_basis v v'
 #align mk_eq_mk_of_basis' mk_eq_mk_of_basis'
 
@@ -604,7 +604,7 @@ Another auxiliary lemma for `Basis.le_span`, which does not require assuming the
 but still assumes we have a finite spanning set.
 -/
 theorem basis_le_span' {ι : Type _} (b : Basis ι R M) {w : Set M} [Fintype w] (s : span R w = ⊤) :
-    (#ι) ≤ Fintype.card w := by
+    #ι ≤ Fintype.card w := by
   haveI := nontrivial_of_invariantBasisNumber R
   haveI := basisFintypeOfFiniteSpans w s b
   rw [Cardinal.mk_fintype ι]
@@ -617,7 +617,7 @@ theorem basis_le_span' {ι : Type _} (b : Basis ι R M) {w : Set M} [Fintype w]
 /-- If `R` satisfies the rank condition,
 then the cardinality of any basis is bounded by the cardinality of any spanning set.
 -/
-theorem Basis.le_span {J : Set M} (v : Basis ι R M) (hJ : span R J = ⊤) : (#range v) ≤ (#J) := by
+theorem Basis.le_span {J : Set M} (v : Basis ι R M) (hJ : span R J = ⊤) : #(range v) ≤ #J := by
   haveI := nontrivial_of_invariantBasisNumber R
   cases fintypeOrInfinite J
   · rw [← Cardinal.lift_le, Cardinal.mk_range_eq_of_injective v.injective, Cardinal.mk_fintype J]
@@ -637,7 +637,7 @@ theorem Basis.le_span {J : Set M} (v : Basis ι R M) (hJ : span R J = ⊤) : (#r
         rcases mem_iUnion.1 (this (Finset.mem_singleton_self _)) with ⟨j, hj⟩
         exact mem_iUnion.2 ⟨j, (mem_image _ _ _).2 ⟨i, hj, rfl⟩⟩
     refine' le_of_not_lt fun IJ => _
-    suffices (#⋃ j, S' j) < (#range v) by exact not_le_of_lt this ⟨Set.embeddingOfSubset _ _ hs⟩
+    suffices #(⋃ j, S' j) < #(range v) by exact not_le_of_lt this ⟨Set.embeddingOfSubset _ _ hs⟩
     refine' lt_of_le_of_lt (le_trans Cardinal.mk_iUnion_le_sum_mk
       (Cardinal.sum_le_sum _ (fun _ => ℵ₀) _)) _
     · exact fun j => (Cardinal.lt_aleph0_of_finite _).le
@@ -693,7 +693,7 @@ contained in the span of some finite `w : Set M`,
 the cardinality of `ι` is bounded by the cardinality of `w`.
 -/
 theorem linearIndependent_le_span' {ι : Type _} (v : ι → M) (i : LinearIndependent R v) (w : Set M)
-    [Fintype w] (s : range v ≤ span R w) : (#ι) ≤ Fintype.card w := by
+    [Fintype w] (s : range v ≤ span R w) : #ι ≤ Fintype.card w := by
   haveI : Fintype ι := linearIndependentFintypeOfLeSpanFintype v i w s
   rw [Cardinal.mk_fintype]
   simp only [Cardinal.natCast_le]
@@ -706,7 +706,7 @@ and any finite spanning set `w : Set M`,
 the cardinality of `ι` is bounded by the cardinality of `w`.
 -/
 theorem linearIndependent_le_span {ι : Type _} (v : ι → M) (i : LinearIndependent R v) (w : Set M)
-    [Fintype w] (s : span R w = ⊤) : (#ι) ≤ Fintype.card w := by
+    [Fintype w] (s : span R w = ⊤) : #ι ≤ Fintype.card w := by
   apply linearIndependent_le_span' v i w
   rw [s]
   exact le_top
@@ -714,7 +714,7 @@ theorem linearIndependent_le_span {ι : Type _} (v : ι → M) (i : LinearIndepe
 
 /-- A version of `linearIndependent_le_span` for `Finset`. -/
 theorem linearIndependent_le_span_finset {ι : Type _} (v : ι → M) (i : LinearIndependent R v)
-    (w : Finset M) (s : span R (w : Set M) = ⊤) : (#ι) ≤ w.card := by
+    (w : Finset M) (s : span R (w : Set M) = ⊤) : #ι ≤ w.card := by
   simpa only [Finset.coe_sort_coe, Fintype.card_coe] using linearIndependent_le_span v i w s
 #align linear_independent_le_span_finset linearIndependent_le_span_finset
 
@@ -722,7 +722,7 @@ theorem linearIndependent_le_span_finset {ι : Type _} (v : ι → M) (i : Linea
 we handle the case where the basis `b` is infinite.
 -/
 theorem linearIndependent_le_infinite_basis {ι : Type _} (b : Basis ι R M) [Infinite ι] {κ : Type _}
-    (v : κ → M) (i : LinearIndependent R v) : (#κ) ≤ (#ι) := by
+    (v : κ → M) (i : LinearIndependent R v) : #κ ≤ #ι := by
   by_contra h
   rw [not_le, ← Cardinal.mk_finset_of_infinite ι] at h
   let Φ := fun k : κ => (b.repr (v k)).support
@@ -743,7 +743,7 @@ and `s` is a linearly independent set,
 then the cardinality of `s` is bounded by the cardinality of `b`.
 -/
 theorem linearIndependent_le_basis {ι : Type _} (b : Basis ι R M) {κ : Type _} (v : κ → M)
-    (i : LinearIndependent R v) : (#κ) ≤ (#ι) := by
+    (i : LinearIndependent R v) : #κ ≤ #ι := by
   -- We split into cases depending on whether `ι` is infinite.
   cases fintypeOrInfinite ι
   · rw [Cardinal.mk_fintype ι] -- When `ι` is finite, we have `linearIndependent_le_span`,
@@ -770,14 +770,14 @@ This proof (along with some of the lemmas above) comes from
 [Les familles libres maximales d'un module ont-elles le meme cardinal?][lazarus1973]
 -/
 theorem maximal_linearIndependent_eq_infinite_basis {ι : Type _} (b : Basis ι R M) [Infinite ι]
-    {κ : Type _} (v : κ → M) (i : LinearIndependent R v) (m : i.Maximal) : (#κ) = (#ι) := by
+    {κ : Type _} (v : κ → M) (i : LinearIndependent R v) (m : i.Maximal) : #κ = #ι := by
   apply le_antisymm
   · exact linearIndependent_le_basis b v i
   · haveI : Nontrivial R := nontrivial_of_invariantBasisNumber R
     exact infinite_basis_le_maximal_linearIndependent b v i m
 #align maximal_linear_independent_eq_infinite_basis maximal_linearIndependent_eq_infinite_basis
 
-theorem Basis.mk_eq_rank'' {ι : Type v} (v : Basis ι R M) : (#ι) = Module.rank R M := by
+theorem Basis.mk_eq_rank'' {ι : Type v} (v : Basis ι R M) : #ι = Module.rank R M := by
   haveI := nontrivial_of_invariantBasisNumber R
   rw [Module.rank_def]
   apply le_antisymm
@@ -795,7 +795,7 @@ theorem Basis.mk_eq_rank'' {ι : Type v} (v : Basis ι R M) : (#ι) = Module.ran
     apply linearIndependent_le_basis v _ li
 #align basis.mk_eq_rank'' Basis.mk_eq_rank''
 
-theorem Basis.mk_range_eq_rank (v : Basis ι R M) : (#range v) = Module.rank R M :=
+theorem Basis.mk_range_eq_rank (v : Basis ι R M) : #(range v) = Module.rank R M :=
   v.reindexRange.mk_eq_rank''
 #align basis.mk_range_eq_rank Basis.mk_range_eq_rank
 
@@ -827,13 +827,13 @@ theorem Basis.card_le_card_of_le {N O : Submodule R M} (hNO : N ≤ O) [Fintype
 #align basis.card_le_card_of_le Basis.card_le_card_of_le
 
 theorem Basis.mk_eq_rank (v : Basis ι R M) :
-    Cardinal.lift.{v} (#ι) = Cardinal.lift.{w} (Module.rank R M) := by
+    Cardinal.lift.{v} #ι = Cardinal.lift.{w} (Module.rank R M) := by
   haveI := nontrivial_of_invariantBasisNumber R
   rw [← v.mk_range_eq_rank, Cardinal.mk_range_eq_of_injective v.injective]
 #align basis.mk_eq_rank Basis.mk_eq_rank
 
 theorem Basis.mk_eq_rank'.{m} (v : Basis ι R M) :
-    Cardinal.lift.{max v m} (#ι) = Cardinal.lift.{max w m} (Module.rank R M) :=
+    Cardinal.lift.{max v m} #ι = Cardinal.lift.{max w m} (Module.rank R M) :=
   Cardinal.lift_umax_eq.{w, v, m}.mpr v.mk_eq_rank
 #align basis.mk_eq_rank' Basis.mk_eq_rank'
 
@@ -857,14 +857,14 @@ theorem Basis.finite_index_of_rank_lt_aleph0 {ι : Type _} {s : Set ι} (b : Bas
 #align basis.finite_index_of_rank_lt_aleph_0 Basis.finite_index_of_rank_lt_aleph0
 
 theorem rank_span {v : ι → M} (hv : LinearIndependent R v) :
-    Module.rank R ↑(span R (range v)) = (#range v) := by
+    Module.rank R ↑(span R (range v)) = #(range v) := by
   haveI := nontrivial_of_invariantBasisNumber R
   rw [← Cardinal.lift_inj, ← (Basis.span hv).mk_eq_rank,
     Cardinal.mk_range_eq_of_injective (@LinearIndependent.injective ι R M v _ _ _ _ hv)]
 #align rank_span rank_span
 
 theorem rank_span_set {s : Set M} (hs : LinearIndependent R (fun x => x : s → M)) :
-    Module.rank R ↑(span R s) = (#s) := by
+    Module.rank R ↑(span R s) = #s := by
   rw [← @setOf_mem_eq _ s, ← Subtype.range_coe_subtype]
   exact rank_span hs
 #align rank_span_set rank_span_set
@@ -924,7 +924,7 @@ namespace Module.Free
 variable (K V)
 
 /-- The rank of a free module `M` over `R` is the cardinality of `ChooseBasisIndex R M`. -/
-theorem rank_eq_card_chooseBasisIndex : Module.rank K V = (#ChooseBasisIndex K V) :=
+theorem rank_eq_card_chooseBasisIndex : Module.rank K V = #(ChooseBasisIndex K V) :=
   (chooseBasis K V).mk_eq_rank''.symm
 #align module.free.rank_eq_card_choose_basis_index Module.Free.rank_eq_card_chooseBasisIndex
 
@@ -940,7 +940,7 @@ theorem nonempty_linearEquiv_of_lift_rank_eq
     Nonempty (V ≃ₗ[K] V') := by
   obtain ⟨⟨_, B⟩⟩ := Module.Free.exists_basis (R := K) (M := V)
   obtain ⟨⟨_, B'⟩⟩ := Module.Free.exists_basis (R := K) (M := V')
-  have : Cardinal.lift.{v', v} (#_) = Cardinal.lift.{v, v'} (#_) := by
+  have : Cardinal.lift.{v', v} #_ = Cardinal.lift.{v, v'} #_ := by
     rw [B.mk_eq_rank'', cnd, B'.mk_eq_rank'']
   exact (Cardinal.lift_mk_eq.{v, v', 0}.1 this).map (B.equiv B')
 #align nonempty_linear_equiv_of_lift_rank_eq nonempty_linearEquiv_of_lift_rank_eq
@@ -1066,7 +1066,7 @@ theorem Basis.finite_ofVectorSpaceIndex_of_rank_lt_aleph0 (h : Module.rank K V <
 -- TODO how far can we generalise this?
 -- When `s` is finite, we could prove this for any ring satisfying the strong rank condition
 -- using `linearIndependent_le_span'`
-theorem rank_span_le (s : Set V) : Module.rank K (span K s) ≤ (#s) := by
+theorem rank_span_le (s : Set V) : Module.rank K (span K s) ≤ #s := by
   obtain ⟨b, hb, hsab, hlib⟩ := exists_linearIndependent K s
   convert Cardinal.mk_le_mk_of_subset hb
   rw [← hsab, rank_span_set hlib]
@@ -1074,7 +1074,7 @@ theorem rank_span_le (s : Set V) : Module.rank K (span K s) ≤ (#s) := by
 
 theorem rank_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V)) < ℵ₀ :=
   calc
-    Module.rank K (span K (↑s : Set V)) ≤ (#(↑s : Set V)) := rank_span_le (s : Set V)
+    Module.rank K (span K (↑s : Set V)) ≤ #(↑s : Set V) := rank_span_le (s : Set V)
     _ = s.card := by rw [Finset.coe_sort_coe, Cardinal.mk_coe_finset]
     _ < ℵ₀ := Cardinal.nat_lt_aleph0 _
 #align rank_span_of_finset rank_span_of_finset
@@ -1184,7 +1184,7 @@ theorem Basis.ofRankEqZero_apply {ι : Type _} [IsEmpty ι] (hV : Module.rank K
 #align basis.of_rank_eq_zero_apply Basis.ofRankEqZero_apply
 
 theorem le_rank_iff_exists_linearIndependent {c : Cardinal} :
-    c ≤ Module.rank K V ↔ ∃ s : Set V, (#s) = c ∧ LinearIndependent K ((↑) : s → V) := by
+    c ≤ Module.rank K V ↔ ∃ s : Set V, #s = c ∧ LinearIndependent K ((↑) : s → V) := by
   constructor
   · intro h
     let t := Basis.ofVectorSpace K V
@@ -1387,7 +1387,7 @@ theorem rank_finset_sum_le {η} (s : Finset η) (f : η → V →ₗ[K] V') :
 #align linear_map.rank_finset_sum_le LinearMap.rank_finset_sum_le
 
 theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'} :
-    c ≤ rank f ↔ ∃ s : Set V, Cardinal.lift.{v'} (#s) =
+    c ≤ rank f ↔ ∃ s : Set V, Cardinal.lift.{v'} #s =
     Cardinal.lift.{v} c ∧ LinearIndependent K fun x : s => f x := by
   rcases f.rangeRestrict.exists_rightInverse_of_surjective f.range_rangeRestrict with ⟨g, hg⟩
   have fg : LeftInverse f.rangeRestrict g := LinearMap.congr_fun hg

@@ -108,7 +108,7 @@ The definition is marked as protected to avoid conflicts with `_root_.rank`,
 the rank of a linear map.
 -/
 protected irreducible_def Module.rank : Cardinal :=
-  ⨆ ι : { s : Set V // LinearIndependent K ((↑) : s → V) }, #ι.1
+  ⨆ ι : { s : Set V // LinearIndependent K ((↑) : s → V) }, (#ι.1)
 #align module.rank Module.rank
 
 end
@@ -358,7 +358,7 @@ then the union of the supports of `x ∈ s` (when written out in the basis `b`)
 -/
 theorem union_support_maximal_linearIndependent_eq_range_basis {ι : Type w} (b : Basis ι R M)
     {κ : Type w'} (v : κ → M) (i : LinearIndependent R v) (m : i.Maximal) :
-    (⋃ k, ((b.repr (v k)).support : Set ι)) = Set.univ := by
+    ⋃ k, ((b.repr (v k)).support : Set ι) = Set.univ := by
   -- If that's not the case,
   by_contra h
   simp only [← Ne.def, ne_univ_iff_exists_not_mem, mem_iUnion, not_exists_not,

Changes are of the form

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

@@ -404,7 +404,7 @@ theorem union_support_maximal_linearIndependent_eq_range_basis {ι : Type w} (b
     have l₀ : l none = 0 := by
       rw [← eq_neg_iff_add_eq_zero] at z
       replace z := neg_eq_iff_eq_neg.mpr z
-      apply_fun fun x => b.repr x b'  at z
+      apply_fun fun x => b.repr x b' at z
       simp only [repr_self, LinearEquiv.map_smul, mul_one, Finsupp.single_eq_same, Pi.neg_apply,
         Finsupp.smul_single', LinearEquiv.map_neg, Finsupp.coe_neg] at z
       erw [FunLike.congr_fun (Finsupp.apply_total R (b.repr : M →ₗ[R] ι →₀ R) v l.some) b'] at z
@@ -889,7 +889,7 @@ theorem Ideal.rank_eq {R S : Type _} [CommRing R] [StrongRankCondition R] [Ring
   obtain ⟨a, ha⟩ := Submodule.nonzero_mem_of_bot_lt (bot_lt_iff_ne_bot.mpr hI)
   have : LinearIndependent R fun i => b i • a := by
     have hb := b.linearIndependent
-    rw [Fintype.linearIndependent_iff] at hb⊢
+    rw [Fintype.linearIndependent_iff] at hb ⊢
     intro g hg
     apply hb g
     simp only [← smul_assoc, ← Finset.sum_smul, smul_eq_zero] at hg
@@ -1130,7 +1130,7 @@ theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd
     rintro ⟨d, e⟩
     have h := eq₂ d (-e)
     simp only [add_eq_zero_iff_eq_neg, LinearMap.prod_apply, mem_ker, SetLike.mem_coe,
-      Prod.mk.inj_iff, coprod_apply, map_neg, neg_apply, LinearMap.mem_range, Pi.prod] at h⊢
+      Prod.mk.inj_iff, coprod_apply, map_neg, neg_apply, LinearMap.mem_range, Pi.prod] at h ⊢
     intro hde
     rcases h hde with ⟨c, h₁, h₂⟩
     refine' ⟨c, h₁, _⟩
@@ -1272,7 +1272,7 @@ theorem rank_submodule_le_one_iff' (s : Submodule K V) :
         rintro rfl
         simp at hw0
       rwa [span_singleton_smul_eq (IsUnit.mk0 _ h0) _]
-    · push_neg  at hw
+    · push_neg at hw
       rw [← Submodule.eq_bot_iff] at hw
       simp [hw]
 #align rank_submodule_le_one_iff' rank_submodule_le_one_iff'

Cardinal.lift_le and Cardinal.lift_mk_le have their universes out of order, in the sense that persistently through the rest of the library we need to specify the 2nd universe (resp 3rd), while the others are solved by unification.

This PR reorders the universes so it's easier to specify the thing you need to specify!

(This PR doesn't get rid of all the occurrences of \.\{_, in the library, but I'd like to do that later.)

I do have a hidden agenda here, which is that I've been experimenting with solutions to the dreaded "Can't solve max u v = max v ?u" universe unification issue (which is making life hellish forward porting https://github.com/leanprover-community/mathlib/pull/19153), and my favourite (but still hacky) solution doesn't like some of the occasions where we reference a lemma filling in some of its universe arguments with _ but then fully specify a later one. (e.g. rw [← lift_le.{_, max u v}, lift_lift, lift_mk_le.{_, _, v}] in ModelTheory/Skolem.lean). Hence the cleanup proposed in this PR makes my life easier working on these experiments. :-)

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

@@ -621,7 +621,7 @@ theorem Basis.le_span {J : Set M} (v : Basis ι R M) (hJ : span R J = ⊤) : (#r
   haveI := nontrivial_of_invariantBasisNumber R
   cases fintypeOrInfinite J
   · rw [← Cardinal.lift_le, Cardinal.mk_range_eq_of_injective v.injective, Cardinal.mk_fintype J]
-    convert Cardinal.lift_le.{w, v}.2 (basis_le_span' v hJ)
+    convert Cardinal.lift_le.{v}.2 (basis_le_span' v hJ)
     simp
   · let S : J → Set ι := fun j => ↑(v.repr j).support
     let S' : J → Set M := fun j => v '' S j

Part 2 of #5001

@@ -589,7 +589,7 @@ the cardinality of `ι` is bounded by the cardinality of `w`.
 -/
 theorem Basis.le_span'' {ι : Type _} [Fintype ι] (b : Basis ι R M) {w : Set M} [Fintype w]
     (s : span R w = ⊤) : Fintype.card ι ≤ Fintype.card w := by
-  -- We construct an surjective linear map `(w → R) →ₗ[R] (ι → R)`,
+  -- We construct a surjective linear map `(w → R) →ₗ[R] (ι → R)`,
   -- by expressing a linear combination in `w` as a linear combination in `ι`.
   fapply card_le_of_surjective' R
   · exact b.repr.toLinearMap.comp (Finsupp.total w M R (↑))

These are all doc fixes

@@ -750,7 +750,7 @@ theorem linearIndependent_le_basis {ι : Type _} (b : Basis ι R M) {κ : Type _
     haveI : Nontrivial R := nontrivial_of_invariantBasisNumber R
     rw [Fintype.card_congr (Equiv.ofInjective b b.injective)]
     exact linearIndependent_le_span v i (range b) b.span_eq
-  · -- and otherwise we have `linearIndepedent_le_infinite_basis`.
+  · -- and otherwise we have `linearIndependent_le_infinite_basis`.
     exact linearIndependent_le_infinite_basis b v i
 #align linear_independent_le_basis linearIndependent_le_basis
 

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

@@ -48,7 +48,7 @@ For modules over rings satisfying the strong rank condition
 
 * `linearIndependent_le_span`:
   For any linearly independent family `v : ι → M`
-  and any finite spanning set `w : set M`,
+  and any finite spanning set `w : Set M`,
   the cardinality of `ι` is bounded by the cardinality of `w`.
 * `linearIndependent_le_basis`:
   If `b` is a basis for a module `M`,

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>

@@ -123,7 +123,6 @@ variable {M' : Type v'} [AddCommGroup M'] [Module R M']
 
 variable {M₁ : Type v} [AddCommGroup M₁] [Module R M₁]
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem LinearMap.lift_rank_le_of_injective (f : M →ₗ[R] M') (i : Injective f) :
     Cardinal.lift.{v'} (Module.rank R M) ≤ Cardinal.lift.{v} (Module.rank R M') := by
   simp only [Module.rank_def]
@@ -135,7 +134,6 @@ theorem LinearMap.lift_rank_le_of_injective (f : M →ₗ[R] M') (i : Injective
   exact (li.map' _ <| LinearMap.ker_eq_bot.mpr i).image
 #align linear_map.lift_rank_le_of_injective LinearMap.lift_rank_le_of_injective
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem LinearMap.rank_le_of_injective (f : M →ₗ[R] M₁) (i : Injective f) :
     Module.rank R M ≤ Module.rank R M₁ :=
   Cardinal.lift_le.1 (f.lift_rank_le_of_injective i)
@@ -151,7 +149,6 @@ theorem rank_le {n : ℕ}
 #align rank_le rank_le
 
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- The rank of the range of a linear map is at most the rank of the source. -/
 -- The proof is: a free submodule of the range lifts to a free submodule of the
 -- source, by arbitrarily lifting a basis.
@@ -170,19 +167,16 @@ theorem lift_rank_range_le (f : M →ₗ[R] M') : Cardinal.lift.{v}
   · exact (Cardinal.lift_mk_eq'.mpr ⟨Equiv.Set.rangeSplittingImageEquiv f s⟩).ge
 #align lift_rank_range_le lift_rank_range_le
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem rank_range_le (f : M →ₗ[R] M₁) : Module.rank R (LinearMap.range f) ≤ Module.rank R M := by
   simpa using lift_rank_range_le f
 #align rank_range_le rank_range_le
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem lift_rank_map_le (f : M →ₗ[R] M') (p : Submodule R M) :
     Cardinal.lift.{v} (Module.rank R (p.map f)) ≤ Cardinal.lift.{v'} (Module.rank R p) := by
   have h := lift_rank_range_le (f.comp (Submodule.subtype p))
   rwa [LinearMap.range_comp, range_subtype] at h
 #align lift_rank_map_le lift_rank_map_le
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem rank_map_le (f : M →ₗ[R] M₁) (p : Submodule R M) :
     Module.rank R (p.map f) ≤ Module.rank R p := by simpa using lift_rank_map_le f p
 #align rank_map_le rank_map_le
@@ -193,7 +187,6 @@ theorem rank_le_of_submodule (s t : Submodule R M) (h : s ≤ t) :
     Subtype.eq <| show x = y from Subtype.ext_iff_val.1 eq
 #align rank_le_of_submodule rank_le_of_submodule
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- Two linearly equivalent vector spaces have the same dimension, a version with different
 universes. -/
 theorem LinearEquiv.lift_rank_eq (f : M ≃ₗ[R] M') :
@@ -203,19 +196,16 @@ theorem LinearEquiv.lift_rank_eq (f : M ≃ₗ[R] M') :
   · exact f.symm.toLinearMap.lift_rank_le_of_injective f.symm.injective
 #align linear_equiv.lift_rank_eq LinearEquiv.lift_rank_eq
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- Two linearly equivalent vector spaces have the same dimension. -/
 theorem LinearEquiv.rank_eq (f : M ≃ₗ[R] M₁) : Module.rank R M = Module.rank R M₁ :=
   Cardinal.lift_inj.1 f.lift_rank_eq
 #align linear_equiv.rank_eq LinearEquiv.rank_eq
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem rank_eq_of_injective (f : M →ₗ[R] M₁) (h : Injective f) :
     Module.rank R M = Module.rank R (LinearMap.range f) :=
   (LinearEquiv.ofInjective f h).rank_eq
 #align rank_eq_of_injective rank_eq_of_injective
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- Pushforwards of submodules along a `LinearEquiv` have the same dimension. -/
 theorem LinearEquiv.rank_map_eq (f : M ≃ₗ[R] M₁) (p : Submodule R M) :
     Module.rank R (p.map (f : M →ₗ[R] M₁)) = Module.rank R p :=
@@ -224,7 +214,6 @@ theorem LinearEquiv.rank_map_eq (f : M ≃ₗ[R] M₁) (p : Submodule R M) :
 
 variable (R M)
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 @[simp]
 theorem rank_top : Module.rank R (⊤ : Submodule R M) = Module.rank R M := by
   have : (⊤ : Submodule R M) ≃ₗ[R] M := LinearEquiv.ofTop ⊤ rfl
@@ -233,7 +222,6 @@ theorem rank_top : Module.rank R (⊤ : Submodule R M) = Module.rank R M := by
 
 variable {R M}
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem rank_range_of_surjective (f : M →ₗ[R] M') (h : Surjective f) :
     Module.rank R (LinearMap.range f) = Module.rank R M' :=
   by rw [LinearMap.range_eq_top.2 h, rank_top]
@@ -244,7 +232,6 @@ theorem rank_submodule_le (s : Submodule R M) : Module.rank R s ≤ Module.rank
   exact rank_le_of_submodule _ _ le_top
 #align rank_submodule_le rank_submodule_le
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem LinearMap.rank_le_of_surjective (f : M →ₗ[R] M₁) (h : Surjective f) :
     Module.rank R M₁ ≤ Module.rank R M := by
   rw [← rank_range_of_surjective f h]
@@ -297,7 +284,6 @@ theorem rank_punit : Module.rank R PUnit = 0 := by
   simpa using LinearIndependent.ne_zero (⟨a, ha⟩ : s) li
 #align rank_punit rank_punit
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 @[simp]
 theorem rank_bot : Module.rank R (⊥ : Submodule R M) = 0 := by
   have : (⊥ : Submodule R M) ≃ₗ[R] PUnit := botEquivPUnit
@@ -328,7 +314,6 @@ theorem LinearIndependent.set_finite_of_isNoetherian [IsNoetherian R M] {s : Set
   @Set.toFinite _ _ hi.finite_of_isNoetherian
 #align linear_independent.set_finite_of_is_noetherian LinearIndependent.set_finite_of_isNoetherian
 
-set_option synthInstance.etaExperiment true in
 -- One might hope that a finite spanning set implies that any linearly independent set is finite.
 -- While this is true over a division ring
 -- (simply because any linearly independent set can be extended to a basis),
@@ -366,7 +351,6 @@ def basisFintypeOfFiniteSpans (w : Set M) [Fintype w] (s : span R w = ⊤) {ι :
   exact nm
 #align basis_fintype_of_finite_spans basisFintypeOfFiniteSpans
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 -- From [Les familles libres maximales d'un module ont-elles le meme cardinal?][lazarus1973]
 /-- Over any ring `R`, if `b` is a basis for a module `M`,
 and `s` is a maximal linearly independent set,
@@ -550,7 +534,6 @@ variable {R : Type u} [Ring R] [InvariantBasisNumber R]
 
 variable {M : Type v} [AddCommGroup M] [Module R M]
 
-set_option synthInstance.etaExperiment true in
 /-- The dimension theorem: if `v` and `v'` are two bases, their index types
 have the same cardinalities. -/
 theorem mk_eq_mk_of_basis (v : Basis ι R M) (v' : Basis ι' R M) :
@@ -597,7 +580,6 @@ variable {R : Type u} [Ring R] [RankCondition R]
 
 variable {M : Type v} [AddCommGroup M] [Module R M]
 
-set_option synthInstance.etaExperiment true in
 /-- An auxiliary lemma for `Basis.le_span`.
 
 If `R` satisfies the rank condition,
@@ -630,7 +612,6 @@ theorem basis_le_span' {ι : Type _} (b : Basis ι R M) {w : Set M} [Fintype w]
   exact Basis.le_span'' b s
 #align basis_le_span' basis_le_span'
 
-set_option synthInstance.etaExperiment true in
 -- Note that if `R` satisfies the strong rank condition,
 -- this also follows from `linearIndependent_le_span` below.
 /-- If `R` satisfies the rank condition,
@@ -673,7 +654,6 @@ variable {M : Type v} [AddCommGroup M] [Module R M]
 
 open Submodule
 
-set_option synthInstance.etaExperiment true in
 -- An auxiliary lemma for `linearIndependent_le_span'`,
 -- with the additional assumption that the linearly independent family is finite.
 theorem linearIndependent_le_span_aux' {ι : Type _} [Fintype ι] (v : ι → M)
@@ -774,7 +754,6 @@ theorem linearIndependent_le_basis {ι : Type _} (b : Basis ι R M) {κ : Type _
     exact linearIndependent_le_infinite_basis b v i
 #align linear_independent_le_basis linearIndependent_le_basis
 
-set_option synthInstance.etaExperiment true in
 /-- Let `R` satisfy the strong rank condition. If `m` elements of a free rank `n` `R`-module are
 linearly independent, then `m ≤ n`. -/
 theorem Basis.card_le_card_of_linearIndependent_aux {R : Type _} [Ring R] [StrongRankCondition R]
@@ -902,7 +881,6 @@ def Submodule.inductionOnRank [IsDomain R] [Fintype ι] (b : Basis ι R M)
     simpa using b.card_le_card_of_linearIndependent hli
 #align submodule.induction_on_rank Submodule.inductionOnRank
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- If `S` a module-finite free `R`-algebra, then the `R`-rank of a nonzero `R`-free
 ideal `I` of `S` is the same as the rank of `S`. -/
 theorem Ideal.rank_eq {R S : Type _} [CommRing R] [StrongRankCondition R] [Ring S] [IsDomain S]
@@ -924,7 +902,6 @@ theorem Ideal.rank_eq {R S : Type _} [CommRing R] [StrongRankCondition R] [Ring
 
 variable (R)
 
-set_option synthInstance.etaExperiment true in
 @[simp]
 theorem rank_self : Module.rank R R = 1 := by
   rw [← Cardinal.lift_inj, ← (Basis.singleton PUnit R).mk_eq_rank, Cardinal.mk_punit]
@@ -957,7 +934,6 @@ open Module.Free
 
 open Cardinal
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- Two vector spaces are isomorphic if they have the same dimension. -/
 theorem nonempty_linearEquiv_of_lift_rank_eq
     (cnd : Cardinal.lift.{v'} (Module.rank K V) = Cardinal.lift.{v} (Module.rank K V')) :
@@ -969,7 +945,6 @@ theorem nonempty_linearEquiv_of_lift_rank_eq
   exact (Cardinal.lift_mk_eq.{v, v', 0}.1 this).map (B.equiv B')
 #align nonempty_linear_equiv_of_lift_rank_eq nonempty_linearEquiv_of_lift_rank_eq
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- Two vector spaces are isomorphic if they have the same dimension. -/
 theorem nonempty_linearEquiv_of_rank_eq (cond : Module.rank K V = Module.rank K V₁) :
     Nonempty (V ≃ₗ[K] V₁) :=
@@ -980,7 +955,6 @@ section
 
 variable (V V' V₁)
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- Two vector spaces are isomorphic if they have the same dimension. -/
 def LinearEquiv.ofLiftRankEq
     (cond : Cardinal.lift.{v'} (Module.rank K V) = Cardinal.lift.{v} (Module.rank K V')) :
@@ -988,7 +962,6 @@ def LinearEquiv.ofLiftRankEq
   Classical.choice (nonempty_linearEquiv_of_lift_rank_eq cond)
 #align linear_equiv.of_lift_rank_eq LinearEquiv.ofLiftRankEq
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- Two vector spaces are isomorphic if they have the same dimension. -/
 def LinearEquiv.ofRankEq (cond : Module.rank K V = Module.rank K V₁) : V ≃ₗ[K] V₁ :=
   Classical.choice (nonempty_linearEquiv_of_rank_eq cond)
@@ -996,14 +969,12 @@ def LinearEquiv.ofRankEq (cond : Module.rank K V = Module.rank K V₁) : V ≃
 
 end
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- Two vector spaces are isomorphic if and only if they have the same dimension. -/
 theorem LinearEquiv.nonempty_equiv_iff_lift_rank_eq : Nonempty (V ≃ₗ[K] V') ↔
     Cardinal.lift.{v'} (Module.rank K V) = Cardinal.lift.{v} (Module.rank K V') :=
   ⟨fun ⟨h⟩ => LinearEquiv.lift_rank_eq h, fun h => nonempty_linearEquiv_of_lift_rank_eq h⟩
 #align linear_equiv.nonempty_equiv_iff_lift_rank_eq LinearEquiv.nonempty_equiv_iff_lift_rank_eq
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- Two vector spaces are isomorphic if and only if they have the same dimension. -/
 theorem LinearEquiv.nonempty_equiv_iff_rank_eq :
     Nonempty (V ≃ₗ[K] V₁) ↔ Module.rank K V = Module.rank K V₁ :=
@@ -1053,18 +1024,15 @@ theorem rank_fun_eq_lift_mul : Module.rank K (η → V) =
   by rw [rank_pi, Cardinal.sum_const, Cardinal.mk_fintype, Cardinal.lift_natCast]
 #align rank_fun_eq_lift_mul rank_fun_eq_lift_mul
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem rank_fun' : Module.rank K (η → K) = Fintype.card η := by
   rw [rank_fun_eq_lift_mul, rank_self, Cardinal.lift_one, mul_one, Cardinal.natCast_inj]
 #align rank_fun' rank_fun'
 
-set_option synthInstance.etaExperiment true in
 theorem rank_fin_fun (n : ℕ) : Module.rank K (Fin n → K) = n := by simp [rank_fun']
 #align rank_fin_fun rank_fin_fun
 
 end Fintype
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 -- TODO: merge with the `Finrank` content
 /-- An `n`-dimensional `K`-vector space is equivalent to `Fin n → K`. -/
 def finDimVectorspaceEquiv (n : ℕ) (hn : Module.rank K V = n) : V ≃ₗ[K] Fin n → K := by
@@ -1118,7 +1086,6 @@ theorem rank_quotient_add_rank (p : Submodule K V) :
     exact rank_prod'.symm.trans f.rank_eq
 #align rank_quotient_add_rank rank_quotient_add_rank
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- rank-nullity theorem -/
 theorem rank_range_add_rank_ker (f : V →ₗ[K] V₁) :
     Module.rank K (LinearMap.range f) + Module.rank K (LinearMap.ker f) = Module.rank K V := by
@@ -1126,7 +1093,6 @@ theorem rank_range_add_rank_ker (f : V →ₗ[K] V₁) :
   rw [← f.quotKerEquivRange.rank_eq, rank_quotient_add_rank]
 #align rank_range_add_rank_ker rank_range_add_rank_ker
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem rank_eq_of_surjective (f : V →ₗ[K] V₁) (h : Surjective f) :
     Module.rank K V = Module.rank K V₁ + Module.rank K (LinearMap.ker f) := by
   rw [← rank_range_add_rank_ker f, ← rank_range_of_surjective f h]
@@ -1140,7 +1106,6 @@ variable [AddCommGroup V₃] [Module K V₃]
 
 open LinearMap
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- This is mostly an auxiliary lemma for `Submodule.rank_sup_add_rank_inf_eq`. -/
 theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd : V₁ →ₗ[K] V₂)
     (ce : V₁ →ₗ[K] V₃) (hde : ⊤ ≤ LinearMap.range db ⊔ LinearMap.range eb) (hgd : ker cd = ⊥)
@@ -1172,7 +1137,6 @@ theorem rank_add_rank_split (db : V₂ →ₗ[K] V) (eb : V₃ →ₗ[K] V) (cd
     rw [h₂, _root_.neg_neg]
 #align rank_add_rank_split rank_add_rank_split
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem Submodule.rank_sup_add_rank_inf_eq (s t : Submodule K V) :
     Module.rank K (s ⊔ t : Submodule K V) + Module.rank K (s ⊓ t : Submodule K V) =
     Module.rank K s + Module.rank K t :=
@@ -1346,7 +1310,6 @@ variable [Ring K] [AddCommGroup V] [Module K V] [AddCommGroup V₁] [Module K V
 
 variable [AddCommGroup V'] [Module K V']
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- `rank f` is the rank of a `LinearMap` `f`, defined as the dimension of `f.range`. -/
 def rank (f : V →ₗ[K] V') : Cardinal :=
   Module.rank K (LinearMap.range f)
@@ -1360,7 +1323,6 @@ theorem rank_le_domain (f : V →ₗ[K] V₁) : rank f ≤ Module.rank K V :=
   rank_range_le _
 #align linear_map.rank_le_domain LinearMap.rank_le_domain
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 @[simp]
 theorem rank_zero [Nontrivial K] : rank (0 : V →ₗ[K] V') = 0 := by
   rw [rank, LinearMap.range_zero, rank_bot]
@@ -1368,20 +1330,17 @@ theorem rank_zero [Nontrivial K] : rank (0 : V →ₗ[K] V') = 0 := by
 
 variable [AddCommGroup V''] [Module K V'']
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem rank_comp_le_left (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') : rank (f.comp g) ≤ rank f := by
   refine' rank_le_of_submodule _ _ _
   rw [LinearMap.range_comp]
   exact LinearMap.map_le_range
 #align linear_map.rank_comp_le_left LinearMap.rank_comp_le_left
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem lift_rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
     Cardinal.lift.{v'} (rank (f.comp g)) ≤ Cardinal.lift.{v''} (rank g) := by
   rw [rank, rank, LinearMap.range_comp]; exact lift_rank_map_le _ _
 #align linear_map.lift_rank_comp_le_right LinearMap.lift_rank_comp_le_right
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- The rank of the composition of two maps is less than the minimum of their ranks. -/
 theorem lift_rank_comp_le (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
     Cardinal.lift.{v'} (rank (f.comp g)) ≤
@@ -1391,12 +1350,10 @@ theorem lift_rank_comp_le (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
 
 variable [AddCommGroup V'₁] [Module K V'₁]
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) : rank (f.comp g) ≤ rank g := by
   simpa only [Cardinal.lift_id] using lift_rank_comp_le_right g f
 #align linear_map.rank_comp_le_right LinearMap.rank_comp_le_right
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 /-- The rank of the composition of two maps is less than the minimum of their ranks.
 
 See `lift_rank_comp_le` for the universe-polymorphic version. -/
@@ -1413,7 +1370,6 @@ variable [DivisionRing K] [AddCommGroup V] [Module K V] [AddCommGroup V₁] [Mod
 
 variable [AddCommGroup V'] [Module K V']
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
   calc
     rank (f + g) ≤ Module.rank K (LinearMap.range f ⊔ LinearMap.range g : Submodule K V') := by
@@ -1424,14 +1380,12 @@ theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
     _ ≤ rank f + rank g := Submodule.rank_add_le_rank_add_rank _ _
 #align linear_map.rank_add_le LinearMap.rank_add_le
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem rank_finset_sum_le {η} (s : Finset η) (f : η → V →ₗ[K] V') :
     rank (∑ d in s, f d) ≤ ∑ d in s, rank (f d) :=
   @Finset.sum_hom_rel _ _ _ _ _ (fun a b => rank a ≤ b) f (fun d => rank (f d)) s
     (le_of_eq rank_zero) fun _ _ _ h => le_trans (rank_add_le _ _) (add_le_add_left h _)
 #align linear_map.rank_finset_sum_le LinearMap.rank_finset_sum_le
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'} :
     c ≤ rank f ↔ ∃ s : Set V, Cardinal.lift.{v'} (#s) =
     Cardinal.lift.{v} c ∧ LinearIndependent K fun x : s => f x := by
@@ -1454,7 +1408,6 @@ theorem le_rank_iff_exists_linearIndependent {c : Cardinal} {f : V →ₗ[K] V'}
     exact injOn_iff_injective.2 this.injective
 #align linear_map.le_rank_iff_exists_linear_independent LinearMap.le_rank_iff_exists_linearIndependent
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem le_rank_iff_exists_linearIndependent_finset {n : ℕ} {f : V →ₗ[K] V'} :
     ↑n ≤ rank f ↔ ∃ s : Finset V, s.card = n ∧ LinearIndependent K fun x : (s : Set V) => f x := by
   simp only [le_rank_iff_exists_linearIndependent, Cardinal.lift_natCast, Cardinal.lift_eq_nat_iff,

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>

@@ -127,9 +127,9 @@ set_option synthInstance.etaExperiment true in -- Porting note: gets around lean
 theorem LinearMap.lift_rank_le_of_injective (f : M →ₗ[R] M') (i : Injective f) :
     Cardinal.lift.{v'} (Module.rank R M) ≤ Cardinal.lift.{v} (Module.rank R M') := by
   simp only [Module.rank_def]
-  rw [Cardinal.lift_supᵢ (Cardinal.bddAbove_range.{v', v'} _),
-    Cardinal.lift_supᵢ (Cardinal.bddAbove_range.{v, v} _)]
-  apply csupᵢ_mono' (Cardinal.bddAbove_range.{v', v} _)
+  rw [Cardinal.lift_iSup (Cardinal.bddAbove_range.{v', v'} _),
+    Cardinal.lift_iSup (Cardinal.bddAbove_range.{v, v} _)]
+  apply ciSup_mono' (Cardinal.bddAbove_range.{v', v} _)
   rintro ⟨s, li⟩
   refine' ⟨⟨f '' s, _⟩, Cardinal.lift_mk_le'.mpr ⟨(Equiv.Set.image f s i).toEmbedding⟩⟩
   exact (li.map' _ <| LinearMap.ker_eq_bot.mpr i).image
@@ -145,7 +145,7 @@ theorem rank_le {n : ℕ}
     (H : ∀ s : Finset M, (LinearIndependent R fun i : s => (i : M)) → s.card ≤ n) :
     Module.rank R M ≤ n := by
   rw [Module.rank_def]
-  apply csupᵢ_le'
+  apply ciSup_le'
   rintro ⟨s, li⟩
   exact linearIndependent_bounded_of_finset_linearIndependent_bounded H _ li
 #align rank_le rank_le
@@ -158,13 +158,13 @@ set_option synthInstance.etaExperiment true in -- Porting note: gets around lean
 theorem lift_rank_range_le (f : M →ₗ[R] M') : Cardinal.lift.{v}
     (Module.rank R (LinearMap.range f)) ≤ Cardinal.lift.{v'} (Module.rank R M) := by
   simp only [Module.rank_def]
-  rw [Cardinal.lift_supᵢ (Cardinal.bddAbove_range.{v', v'} _)]
-  apply csupᵢ_le'
+  rw [Cardinal.lift_iSup (Cardinal.bddAbove_range.{v', v'} _)]
+  apply ciSup_le'
   rintro ⟨s, li⟩
   apply le_trans
   swap
   · apply Cardinal.lift_le.mpr
-    refine' le_csupᵢ (Cardinal.bddAbove_range.{v, v} _) ⟨rangeSplitting f '' s, _⟩
+    refine' le_ciSup (Cardinal.bddAbove_range.{v, v} _) ⟨rangeSplitting f '' s, _⟩
     apply LinearIndependent.of_comp f.rangeRestrict
     convert li.comp (Equiv.Set.rangeSplittingImageEquiv f s) (Equiv.injective _) using 1
   · exact (Cardinal.lift_mk_eq'.mpr ⟨Equiv.Set.rangeSplittingImageEquiv f s⟩).ge
@@ -265,7 +265,7 @@ theorem cardinal_lift_le_rank_of_linearIndependent {ι : Type w} {v : ι → M}
   · simp only [Cardinal.lift_le, Module.rank_def]
     apply le_trans
     swap
-    · exact le_csupᵢ (Cardinal.bddAbove_range.{v, v} _) ⟨range v, hv.coe_range⟩
+    · exact le_ciSup (Cardinal.bddAbove_range.{v, v} _) ⟨range v, hv.coe_range⟩
     · exact le_rfl
 #align cardinal_lift_le_rank_of_linear_independent cardinal_lift_le_rank_of_linearIndependent
 
@@ -289,7 +289,7 @@ variable (R M)
 @[simp]
 theorem rank_punit : Module.rank R PUnit = 0 := by
   rw [← bot_eq_zero, ← le_bot_iff, Module.rank_def]
-  apply csupᵢ_le'
+  apply ciSup_le'
   rintro ⟨s, li⟩
   rw [le_bot_iff, bot_eq_zero, Cardinal.mk_emptyCollection_iff, Subtype.coe_mk]
   by_contra h
@@ -377,7 +377,7 @@ theorem union_support_maximal_linearIndependent_eq_range_basis {ι : Type w} (b
     (⋃ k, ((b.repr (v k)).support : Set ι)) = Set.univ := by
   -- If that's not the case,
   by_contra h
-  simp only [← Ne.def, ne_univ_iff_exists_not_mem, mem_unionᵢ, not_exists_not,
+  simp only [← Ne.def, ne_univ_iff_exists_not_mem, mem_iUnion, not_exists_not,
     Finsupp.mem_support_iff, Finset.mem_coe] at h
   -- We have some basis element `b b'` which is not in the support of any of the `v i`.
   obtain ⟨b', w⟩ := h
@@ -491,7 +491,7 @@ theorem rank_subsingleton [Subsingleton R] : Module.rank R M = 1 := by
   haveI := Module.subsingleton R M
   have : Nonempty { s : Set M // LinearIndependent R ((↑) : s → M) } :=
     ⟨⟨∅, linearIndependent_empty _ _⟩⟩
-  rw [Module.rank_def, csupᵢ_eq_of_forall_le_of_forall_lt_exists_gt]
+  rw [Module.rank_def, ciSup_eq_of_forall_le_of_forall_lt_exists_gt]
   · rintro ⟨s, hs⟩
     rw [Cardinal.mk_le_one_iff_set_subsingleton]
     apply subsingleton_of_subsingleton
@@ -653,11 +653,11 @@ theorem Basis.le_span {J : Set M} (v : Basis ι R M) (hJ : span R J = ⊤) : (#r
       replace : v.repr (v i) ∈ Finsupp.supported R R (⋃ j, S j) := this trivial
       rw [v.repr_self, Finsupp.mem_supported, Finsupp.support_single_ne_zero _ one_ne_zero] at this
       · subst b
-        rcases mem_unionᵢ.1 (this (Finset.mem_singleton_self _)) with ⟨j, hj⟩
-        exact mem_unionᵢ.2 ⟨j, (mem_image _ _ _).2 ⟨i, hj, rfl⟩⟩
+        rcases mem_iUnion.1 (this (Finset.mem_singleton_self _)) with ⟨j, hj⟩
+        exact mem_iUnion.2 ⟨j, (mem_image _ _ _).2 ⟨i, hj, rfl⟩⟩
     refine' le_of_not_lt fun IJ => _
     suffices (#⋃ j, S' j) < (#range v) by exact not_le_of_lt this ⟨Set.embeddingOfSubset _ _ hs⟩
-    refine' lt_of_le_of_lt (le_trans Cardinal.mk_unionᵢ_le_sum_mk
+    refine' lt_of_le_of_lt (le_trans Cardinal.mk_iUnion_le_sum_mk
       (Cardinal.sum_le_sum _ (fun _ => ℵ₀) _)) _
     · exact fun j => (Cardinal.lt_aleph0_of_finite _).le
     · simpa
@@ -804,14 +804,14 @@ theorem Basis.mk_eq_rank'' {ι : Type v} (v : Basis ι R M) : (#ι) = Module.ran
   apply le_antisymm
   · trans
     swap
-    · apply le_csupᵢ (Cardinal.bddAbove_range.{v, v} _)
+    · apply le_ciSup (Cardinal.bddAbove_range.{v, v} _)
       exact
         ⟨Set.range v, by
           convert v.reindexRange.linearIndependent
           ext
           simp⟩
     · exact (Cardinal.mk_range_eq v v.injective).ge
-  · apply csupᵢ_le'
+  · apply ciSup_le'
     rintro ⟨s, li⟩
     apply linearIndependent_le_basis v _ li
 #align basis.mk_eq_rank'' Basis.mk_eq_rank''

@@ -64,7 +64,7 @@ For modules over rings with invariant basis number
 For vector spaces (i.e. modules over a field), we have
 
 * `rank_quotient_add_rank`: if `V₁` is a submodule of `V`, then
-  `module.rank (V/V₁) + module.rank V₁ = module.rank V`.
+  `Module.rank (V/V₁) + Module.rank V₁ = Module.rank V`.
 * `rank_range_add_rank_ker`: the rank-nullity theorem.
 
 ## Implementation notes
@@ -1011,7 +1011,7 @@ theorem LinearEquiv.nonempty_equiv_iff_rank_eq :
 #align linear_equiv.nonempty_equiv_iff_rank_eq LinearEquiv.nonempty_equiv_iff_rank_eq
 
 /-- If `M` and `N` are free, then the rank of `M × N` is
-`(module.rank R M).lift + (module.rank R N).lift`. -/
+`(Module.rank R M).lift + (Module.rank R N).lift`. -/
 @[simp]
 theorem rank_prod : Module.rank K (V × V') =
     Cardinal.lift.{v'} (Module.rank K V) + Cardinal.lift.{v, v'} (Module.rank K V') := by

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

@@ -1279,14 +1279,14 @@ theorem rank_submodule_le_one_iff (s : Submodule K V) :
     intro v hv
     obtain ⟨r, hr⟩ := h ⟨v, hv⟩
     use r
-    simp_rw [Subtype.ext_iff, coe_smul, Submodule.coe_mk] at hr
+    simp_rw [Subtype.ext_iff, coe_smul] at hr
     exact hr
   · rintro ⟨v₀, hv₀, h⟩
     use ⟨v₀, hv₀⟩
     rintro ⟨v, hv⟩
     obtain ⟨r, hr⟩ := h v hv
     use r
-    simp_rw [Subtype.ext_iff, coe_smul, Submodule.coe_mk]
+    simp_rw [Subtype.ext_iff, coe_smul]
     exact hr
 #align rank_submodule_le_one_iff rank_submodule_le_one_iff
 

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>

@@ -328,6 +328,7 @@ theorem LinearIndependent.set_finite_of_isNoetherian [IsNoetherian R M] {s : Set
   @Set.toFinite _ _ hi.finite_of_isNoetherian
 #align linear_independent.set_finite_of_is_noetherian LinearIndependent.set_finite_of_isNoetherian
 
+set_option synthInstance.etaExperiment true in
 -- One might hope that a finite spanning set implies that any linearly independent set is finite.
 -- While this is true over a division ring
 -- (simply because any linearly independent set can be extended to a basis),
@@ -549,6 +550,7 @@ variable {R : Type u} [Ring R] [InvariantBasisNumber R]
 
 variable {M : Type v} [AddCommGroup M] [Module R M]
 
+set_option synthInstance.etaExperiment true in
 /-- The dimension theorem: if `v` and `v'` are two bases, their index types
 have the same cardinalities. -/
 theorem mk_eq_mk_of_basis (v : Basis ι R M) (v' : Basis ι' R M) :
@@ -595,6 +597,7 @@ variable {R : Type u} [Ring R] [RankCondition R]
 
 variable {M : Type v} [AddCommGroup M] [Module R M]
 
+set_option synthInstance.etaExperiment true in
 /-- An auxiliary lemma for `Basis.le_span`.
 
 If `R` satisfies the rank condition,
@@ -627,6 +630,7 @@ theorem basis_le_span' {ι : Type _} (b : Basis ι R M) {w : Set M} [Fintype w]
   exact Basis.le_span'' b s
 #align basis_le_span' basis_le_span'
 
+set_option synthInstance.etaExperiment true in
 -- Note that if `R` satisfies the strong rank condition,
 -- this also follows from `linearIndependent_le_span` below.
 /-- If `R` satisfies the rank condition,
@@ -669,6 +673,7 @@ variable {M : Type v} [AddCommGroup M] [Module R M]
 
 open Submodule
 
+set_option synthInstance.etaExperiment true in
 -- An auxiliary lemma for `linearIndependent_le_span'`,
 -- with the additional assumption that the linearly independent family is finite.
 theorem linearIndependent_le_span_aux' {ι : Type _} [Fintype ι] (v : ι → M)
@@ -769,6 +774,7 @@ theorem linearIndependent_le_basis {ι : Type _} (b : Basis ι R M) {κ : Type _
     exact linearIndependent_le_infinite_basis b v i
 #align linear_independent_le_basis linearIndependent_le_basis
 
+set_option synthInstance.etaExperiment true in
 /-- Let `R` satisfy the strong rank condition. If `m` elements of a free rank `n` `R`-module are
 linearly independent, then `m ≤ n`. -/
 theorem Basis.card_le_card_of_linearIndependent_aux {R : Type _} [Ring R] [StrongRankCondition R]
@@ -918,6 +924,7 @@ theorem Ideal.rank_eq {R S : Type _} [CommRing R] [StrongRankCondition R] [Ring
 
 variable (R)
 
+set_option synthInstance.etaExperiment true in
 @[simp]
 theorem rank_self : Module.rank R R = 1 := by
   rw [← Cardinal.lift_inj, ← (Basis.singleton PUnit R).mk_eq_rank, Cardinal.mk_punit]
@@ -1051,6 +1058,7 @@ theorem rank_fun' : Module.rank K (η → K) = Fintype.card η := by
   rw [rank_fun_eq_lift_mul, rank_self, Cardinal.lift_one, mul_one, Cardinal.natCast_inj]
 #align rank_fun' rank_fun'
 
+set_option synthInstance.etaExperiment true in
 theorem rank_fin_fun (n : ℕ) : Module.rank K (Fin n → K) = n := by simp [rank_fun']
 #align rank_fin_fun rank_fin_fun
 

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.)

@@ -1414,7 +1414,6 @@ theorem rank_add_le (f g : V →ₗ[K] V') : rank (f + g) ≤ rank f + rank g :=
         show f x + g x ∈ (LinearMap.range f ⊔ LinearMap.range g : Submodule K V') from
         mem_sup.2 ⟨_, ⟨x, rfl⟩, _, ⟨x, rfl⟩, rfl⟩
     _ ≤ rank f + rank g := Submodule.rank_add_le_rank_add_rank _ _
-
 #align linear_map.rank_add_le LinearMap.rank_add_le
 
 set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074

@@ -84,9 +84,7 @@ variable {K : Type u} {V V₁ V₂ V₃ : Type v} {V' V'₁ : Type v'} {V'' : Ty
 
 variable {ι : Type w} {ι' : Type w'} {η : Type u₁'} {φ : η → Type _}
 
-open Classical BigOperators Cardinal
-
-open Basis Submodule Function Set
+open Classical BigOperators Cardinal Basis Submodule Function Set
 
 section Module
 
@@ -165,9 +163,9 @@ theorem lift_rank_range_le (f : M →ₗ[R] M') : Cardinal.lift.{v}
   rintro ⟨s, li⟩
   apply le_trans
   swap
-  apply Cardinal.lift_le.mpr
-  refine' le_csupᵢ (Cardinal.bddAbove_range.{v, v} _) ⟨rangeSplitting f '' s, _⟩
-  · apply LinearIndependent.of_comp f.rangeRestrict
+  · apply Cardinal.lift_le.mpr
+    refine' le_csupᵢ (Cardinal.bddAbove_range.{v, v} _) ⟨rangeSplitting f '' s, _⟩
+    apply LinearIndependent.of_comp f.rangeRestrict
     convert li.comp (Equiv.Set.rangeSplittingImageEquiv f s) (Equiv.injective _) using 1
   · exact (Cardinal.lift_mk_eq'.mpr ⟨Equiv.Set.rangeSplittingImageEquiv f s⟩).ge
 #align lift_rank_range_le lift_rank_range_le
@@ -267,8 +265,8 @@ theorem cardinal_lift_le_rank_of_linearIndependent {ι : Type w} {v : ι → M}
   · simp only [Cardinal.lift_le, Module.rank_def]
     apply le_trans
     swap
-    exact le_csupᵢ (Cardinal.bddAbove_range.{v, v} _) ⟨range v, hv.coe_range⟩
-    exact le_rfl
+    · exact le_csupᵢ (Cardinal.bddAbove_range.{v, v} _) ⟨range v, hv.coe_range⟩
+    · exact le_rfl
 #align cardinal_lift_le_rank_of_linear_independent cardinal_lift_le_rank_of_linearIndependent
 
 theorem cardinal_lift_le_rank_of_linearIndependent' {ι : Type w} {v : ι → M}
@@ -290,13 +288,10 @@ variable (R M)
 
 @[simp]
 theorem rank_punit : Module.rank R PUnit = 0 := by
-  apply le_bot_iff.mp
-  rw [Module.rank_def]
+  rw [← bot_eq_zero, ← le_bot_iff, Module.rank_def]
   apply csupᵢ_le'
   rintro ⟨s, li⟩
-  apply le_bot_iff.mpr
-  apply Cardinal.mk_emptyCollection_iff.mpr
-  simp only [Subtype.coe_mk]
+  rw [le_bot_iff, bot_eq_zero, Cardinal.mk_emptyCollection_iff, Subtype.coe_mk]
   by_contra h
   obtain ⟨a, ha⟩ := nonempty_iff_ne_empty.2 h
   simpa using LinearIndependent.ne_zero (⟨a, ha⟩ : s) li
@@ -803,13 +798,13 @@ theorem Basis.mk_eq_rank'' {ι : Type v} (v : Basis ι R M) : (#ι) = Module.ran
   apply le_antisymm
   · trans
     swap
-    apply le_csupᵢ (Cardinal.bddAbove_range.{v, v} _)
-    exact
-      ⟨Set.range v, by
-        convert v.reindexRange.linearIndependent
-        ext
-        simp⟩
-    exact (Cardinal.mk_range_eq v v.injective).ge
+    · apply le_csupᵢ (Cardinal.bddAbove_range.{v, v} _)
+      exact
+        ⟨Set.range v, by
+          convert v.reindexRange.linearIndependent
+          ext
+          simp⟩
+    · exact (Cardinal.mk_range_eq v v.injective).ge
   · apply csupᵢ_le'
     rintro ⟨s, li⟩
     apply linearIndependent_le_basis v _ li
@@ -915,9 +910,9 @@ theorem Ideal.rank_eq {R S : Type _} [CommRing R] [StrongRankCondition R] [Ring
     apply hb g
     simp only [← smul_assoc, ← Finset.sum_smul, smul_eq_zero] at hg
     exact hg.resolve_right ha
-  exact
-    le_antisymm (b.card_le_card_of_linearIndependent (c.linearIndependent.map' (Submodule.subtype I)
-    ((LinearMap.ker_eq_bot (f := (Submodule.subtype I : I →ₗ[R] S))).mpr Subtype.coe_injective)))
+  exact le_antisymm
+    (b.card_le_card_of_linearIndependent (c.linearIndependent.map' (Submodule.subtype I)
+      ((LinearMap.ker_eq_bot (f := (Submodule.subtype I : I →ₗ[R] S))).mpr Subtype.coe_injective)))
     (c.card_le_card_of_linearIndependent this)
 #align ideal.rank_eq Ideal.rank_eq
 
@@ -1110,9 +1105,9 @@ theorem rank_span_of_finset (s : Finset V) : Module.rank K (span K (↑s : Set V
 
 theorem rank_quotient_add_rank (p : Submodule K V) :
     Module.rank K (V ⧸ p) + Module.rank K p = Module.rank K V := by
-  classical exact
+  classical
     let ⟨f⟩ := quotient_prod_linearEquiv p
-    rank_prod'.symm.trans f.rank_eq
+    exact rank_prod'.symm.trans f.rank_eq
 #align rank_quotient_add_rank rank_quotient_add_rank
 
 set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074

@@ -152,7 +152,11 @@ theorem rank_le {n : ℕ}
   exact linearIndependent_bounded_of_finset_linearIndependent_bounded H _ li
 #align rank_le rank_le
 
+
 set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
+/-- The rank of the range of a linear map is at most the rank of the source. -/
+-- The proof is: a free submodule of the range lifts to a free submodule of the
+-- source, by arbitrarily lifting a basis.
 theorem lift_rank_range_le (f : M →ₗ[R] M') : Cardinal.lift.{v}
     (Module.rank R (LinearMap.range f)) ≤ Cardinal.lift.{v'} (Module.rank R M) := by
   simp only [Module.rank_def]
@@ -770,7 +774,8 @@ theorem linearIndependent_le_basis {ι : Type _} (b : Basis ι R M) {κ : Type _
     exact linearIndependent_le_infinite_basis b v i
 #align linear_independent_le_basis linearIndependent_le_basis
 
-/-- In an `n`-dimensional space, the rank is at most `m`. -/
+/-- Let `R` satisfy the strong rank condition. If `m` elements of a free rank `n` `R`-module are
+linearly independent, then `m ≤ n`. -/
 theorem Basis.card_le_card_of_linearIndependent_aux {R : Type _} [Ring R] [StrongRankCondition R]
     (n : ℕ) {m : ℕ} (v : Fin m → Fin n → R) : LinearIndependent R v → m ≤ n := fun h => by
   simpa using linearIndependent_le_basis (Pi.basisFun R (Fin n)) v h
@@ -884,8 +889,10 @@ theorem rank_span_set {s : Set M} (hs : LinearIndependent R (fun x => x : s →
   exact rank_span hs
 #align rank_span_set rank_span_set
 
-/-- If `N` is a submodule in a free, finitely generated module,
-do induction on adjoining a linear independent element to a submodule. -/
+/-- An induction (and recursion) principle for proving results about all submodules of a fixed
+finite free module `M`. A property is true for all submodules of `M` if it satisfies the following
+"inductive step": the property is true for a submodule `N` if it's true for all submodules `N'`
+of `N` with the property that there exists `0 ≠ x ∈ N` such that the sum `N' + Rx` is direct. -/
 def Submodule.inductionOnRank [IsDomain R] [Fintype ι] (b : Basis ι R M)
     (P : Submodule R M → Sort _) (ih : ∀ N : Submodule R M,
     (∀ N' ≤ N, ∀ x ∈ N, (∀ (c : R), ∀ y ∈ N', c • x + y = (0 : M) → c = 0) → P N') → P N)
@@ -895,9 +902,8 @@ def Submodule.inductionOnRank [IsDomain R] [Fintype ι] (b : Basis ι R M)
 #align submodule.induction_on_rank Submodule.inductionOnRank
 
 set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
-/-- If `S` a finite-dimensional ring extension of `R` which is free as an `R`-module,
-then the rank of an ideal `I` of `S` over `R` is the same as the rank of `S`.
--/
+/-- If `S` a module-finite free `R`-algebra, then the `R`-rank of a nonzero `R`-free
+ideal `I` of `S` is the same as the rank of `S`. -/
 theorem Ideal.rank_eq {R S : Type _} [CommRing R] [StrongRankCondition R] [Ring S] [IsDomain S]
     [Algebra R S] {n m : Type _} [Fintype n] [Fintype m] (b : Basis n R S) {I : Ideal S}
     (hI : I ≠ ⊥) (c : Basis m R I) : Fintype.card m = Fintype.card n := by
@@ -1002,7 +1008,8 @@ theorem LinearEquiv.nonempty_equiv_iff_rank_eq :
   ⟨fun ⟨h⟩ => LinearEquiv.rank_eq h, fun h => nonempty_linearEquiv_of_rank_eq h⟩
 #align linear_equiv.nonempty_equiv_iff_rank_eq LinearEquiv.nonempty_equiv_iff_rank_eq
 
-/-- The rank of `M × N` is `(Module.rank R M).lift + (Module.rank R N).lift`. -/
+/-- If `M` and `N` are free, then the rank of `M × N` is
+`(module.rank R M).lift + (module.rank R N).lift`. -/
 @[simp]
 theorem rank_prod : Module.rank K (V × V') =
     Cardinal.lift.{v'} (Module.rank K V) + Cardinal.lift.{v, v'} (Module.rank K V') := by
@@ -1010,7 +1017,7 @@ theorem rank_prod : Module.rank K (V × V') =
     lift_umax'] using ((chooseBasis K V).prod (chooseBasis K V')).mk_eq_rank.symm
 #align rank_prod rank_prod
 
-/-- If `M` and `N` lie in the same universe, the rank of `M × N` is
+/-- If `M` and `N` are free (and lie in the same universe), the rank of `M × N` is
   `(Module.rank R M) + (Module.rank R N)`. -/
 theorem rank_prod' : Module.rank K (V × V₁) = Module.rank K V + Module.rank K V₁ := by simp
 #align rank_prod' rank_prod'
@@ -1021,7 +1028,8 @@ variable [∀ i, AddCommGroup (φ i)] [∀ i, Module K (φ i)] [∀ i, Module.Fr
 
 open LinearMap
 
-/-- The rank of a finite product is the sum of the ranks. -/
+/-- The rank of a finite product of free modules is the sum of the ranks. -/
+-- this result is not true without the freeness assumption
 @[simp]
 theorem rank_pi [Finite η] : Module.rank K (∀ i, φ i) =
     Cardinal.sum fun i => Module.rank K (φ i) := by

@@ -919,7 +919,7 @@ variable (R)
 
 @[simp]
 theorem rank_self : Module.rank R R = 1 := by
-  rw [← Cardinal.lift_inj, ← (Basis.singleton PUnit R).mk_eq_rank, Cardinal.mk_pUnit]
+  rw [← Cardinal.lift_inj, ← (Basis.singleton PUnit R).mk_eq_rank, Cardinal.mk_punit]
 #align rank_self rank_self
 
 end StrongRankCondition

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 
 ! This file was ported from Lean 3 source module linear_algebra.dimension
-! leanprover-community/mathlib commit b5b5dd5a47b5744260e2c9185013075ce9dadccd
+! leanprover-community/mathlib commit 47a5f8186becdbc826190ced4312f8199f9db6a5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1364,13 +1364,36 @@ theorem rank_comp_le_left (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') : rank (f.
   exact LinearMap.map_le_range
 #align linear_map.rank_comp_le_left LinearMap.rank_comp_le_left
 
+set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
+theorem lift_rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
+    Cardinal.lift.{v'} (rank (f.comp g)) ≤ Cardinal.lift.{v''} (rank g) := by
+  rw [rank, rank, LinearMap.range_comp]; exact lift_rank_map_le _ _
+#align linear_map.lift_rank_comp_le_right LinearMap.lift_rank_comp_le_right
+
+set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
+/-- The rank of the composition of two maps is less than the minimum of their ranks. -/
+theorem lift_rank_comp_le (g : V →ₗ[K] V') (f : V' →ₗ[K] V'') :
+    Cardinal.lift.{v'} (rank (f.comp g)) ≤
+      min (Cardinal.lift.{v'} (rank f)) (Cardinal.lift.{v''} (rank g)) :=
+  le_min (Cardinal.lift_le.mpr <| rank_comp_le_left _ _) (lift_rank_comp_le_right _ _)
+#align linear_map.lift_rank_comp_le LinearMap.lift_rank_comp_le
+
 variable [AddCommGroup V'₁] [Module K V'₁]
 
 set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem rank_comp_le_right (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) : rank (f.comp g) ≤ rank g := by
-  rw [rank, rank, LinearMap.range_comp]; exact rank_map_le _ _
+  simpa only [Cardinal.lift_id] using lift_rank_comp_le_right g f
 #align linear_map.rank_comp_le_right LinearMap.rank_comp_le_right
 
+set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
+/-- The rank of the composition of two maps is less than the minimum of their ranks.
+
+See `lift_rank_comp_le` for the universe-polymorphic version. -/
+theorem rank_comp_le (g : V →ₗ[K] V') (f : V' →ₗ[K] V'₁) :
+    rank (f.comp g) ≤ min (rank f) (rank g) := by
+  simpa only [Cardinal.lift_id] using lift_rank_comp_le g f
+#align linear_map.rank_comp_le LinearMap.rank_comp_le
+
 end Ring
 
 section DivisionRing

• set_theory.cardinal.basic: forward-ports leanprover-community/mathlib#18781, which backports some ad-hoc changes in #3247 in a more principled way
• ring_theory.int.basic: these changes were already forward-ported in #3278, but we forgot the SHA.
• linear_algebra.dimension: forward-ports leanprover-community/mathlib#18792
• linear_algebra.matrix.dot_product: forward-ports leanprover-community/mathlib#18783
• linear_algebra.finrank: forward-ports leanprover-community/mathlib#18794 which is itself a backport of #3378, hence no changes to the file

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Scott Morrison
 
 ! This file was ported from Lean 3 source module linear_algebra.dimension
-! leanprover-community/mathlib commit 45ce3929e3bf9a086a216feea3b1ab6c14bf0e67
+! leanprover-community/mathlib commit b5b5dd5a47b5744260e2c9185013075ce9dadccd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -728,6 +728,12 @@ theorem linearIndependent_le_span {ι : Type _} (v : ι → M) (i : LinearIndepe
   exact le_top
 #align linear_independent_le_span linearIndependent_le_span
 
+/-- A version of `linearIndependent_le_span` for `Finset`. -/
+theorem linearIndependent_le_span_finset {ι : Type _} (v : ι → M) (i : LinearIndependent R v)
+    (w : Finset M) (s : span R (w : Set M) = ⊤) : (#ι) ≤ w.card := by
+  simpa only [Finset.coe_sort_coe, Fintype.card_coe] using linearIndependent_le_span v i w s
+#align linear_independent_le_span_finset linearIndependent_le_span_finset
+
 /-- An auxiliary lemma for `linearIndependent_le_basis`:
 we handle the case where the basis `b` is infinite.
 -/

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Komyyy <pol_tta@outlook.jp>