field_theory.finiteness ⟷ Mathlib.FieldTheory.Finiteness

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: Chris Hughes
 -/
 import RingTheory.Finiteness
-import LinearAlgebra.Dimension
+import LinearAlgebra.Dimension.Basic
 
 #align_import field_theory.finiteness from "leanprover-community/mathlib"@"25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e"
 

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

@@ -50,12 +50,14 @@ theorem iff_rank_lt_aleph0 : IsNoetherian K V ↔ Module.rank K V < ℵ₀ :=
 
 variable (K V)
 
-#print IsNoetherian.rank_lt_aleph0 /-
+/- warning: is_noetherian.rank_lt_aleph_0 clashes with finite_dimensional.rank_lt_aleph_0 -> rank_lt_aleph0
+Case conversion may be inaccurate. Consider using '#align is_noetherian.rank_lt_aleph_0 rank_lt_aleph0ₓ'. -/
+#print rank_lt_aleph0 /-
 /-- The dimension of a noetherian module over a division ring, as a cardinal,
 is strictly less than the first infinite cardinal `ℵ₀`. -/
 theorem rank_lt_aleph0 : ∀ [IsNoetherian K V], Module.rank K V < ℵ₀ :=
   IsNoetherian.iff_rank_lt_aleph0.1
-#align is_noetherian.rank_lt_aleph_0 IsNoetherian.rank_lt_aleph0
+#align is_noetherian.rank_lt_aleph_0 rank_lt_aleph0
 -/
 
 variable {K V}

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

@@ -37,7 +37,8 @@ theorem iff_rank_lt_aleph0 : IsNoetherian K V ↔ Module.rank K V < ℵ₀ :=
   rw [← b.mk_eq_rank'', lt_aleph_0_iff_set_finite]
   constructor
   · intro
-    exact finite_of_linearIndependent (Basis.ofVectorSpaceIndex.linearIndependent K V)
+    exact
+      LinearIndependent.set_finite_of_isNoetherian (Basis.ofVectorSpaceIndex.linearIndependent K V)
   · intro hbfinite
     refine'
       @isNoetherian_of_linearEquiv K (⊤ : Submodule K V) V _ _ _ _ _ (LinearEquiv.ofTop _ rfl)

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

@@ -3,8 +3,8 @@ Copyright (c) 2019 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Mathbin.RingTheory.Finiteness
-import Mathbin.LinearAlgebra.Dimension
+import RingTheory.Finiteness
+import LinearAlgebra.Dimension
 
 #align_import field_theory.finiteness from "leanprover-community/mathlib"@"25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module field_theory.finiteness
-! leanprover-community/mathlib commit 25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Finiteness
 import Mathbin.LinearAlgebra.Dimension
 
+#align_import field_theory.finiteness from "leanprover-community/mathlib"@"25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e"
+
 /-!
 # A module over a division ring is noetherian if and only if it is finite.
 

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

@@ -74,12 +74,14 @@ noncomputable def fintypeBasisIndex {ι : Type _} [IsNoetherian K V] (b : Basis
 noncomputable instance [IsNoetherian K V] : Fintype (Basis.ofVectorSpaceIndex K V) :=
   fintypeBasisIndex (Basis.ofVectorSpace K V)
 
+#print IsNoetherian.finite_basis_index /-
 /-- In a noetherian module over a division ring,
 if a basis is indexed by a set, that set is finite. -/
 theorem finite_basis_index {ι : Type _} {s : Set ι} [IsNoetherian K V] (b : Basis s K V) :
     s.Finite :=
   b.finite_index_of_rank_lt_aleph0 (rank_lt_aleph0 K V)
 #align is_noetherian.finite_basis_index IsNoetherian.finite_basis_index
+-/
 
 variable (K V)
 

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

@@ -134,7 +134,7 @@ theorem iff_fg : IsNoetherian K V ↔ Module.Finite K V :=
   by
   constructor
   · intro h
-    exact ⟨⟨finset_basis_index K V, by convert(finset_basis K V).span_eq; simp⟩⟩
+    exact ⟨⟨finset_basis_index K V, by convert (finset_basis K V).span_eq; simp⟩⟩
   · rintro ⟨s, hs⟩
     rw [IsNoetherian.iff_rank_lt_aleph0, ← rank_top, ← hs]
     exact lt_of_le_of_lt (rank_span_le _) s.finite_to_set.lt_aleph_0

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

@@ -22,7 +22,7 @@ import Mathbin.LinearAlgebra.Dimension
 
 universe u v
 
-open Classical Cardinal
+open scoped Classical Cardinal
 
 open Cardinal Submodule Module Function
 
@@ -30,6 +30,7 @@ namespace IsNoetherian
 
 variable {K : Type u} {V : Type v} [DivisionRing K] [AddCommGroup V] [Module K V]
 
+#print IsNoetherian.iff_rank_lt_aleph0 /-
 /-- A module over a division ring is noetherian if and only if
 its dimension (as a cardinal) is strictly less than the first infinite cardinal `ℵ₀`.
 -/
@@ -47,14 +48,17 @@ theorem iff_rank_lt_aleph0 : IsNoetherian K V ↔ Module.rank K V < ℵ₀ :=
     refine' isNoetherian_of_fg_of_noetherian _ ⟨Set.Finite.toFinset hbfinite, _⟩
     rw [Set.Finite.coe_toFinset, ← b.span_eq, Basis.coe_ofVectorSpace, Subtype.range_coe]
 #align is_noetherian.iff_rank_lt_aleph_0 IsNoetherian.iff_rank_lt_aleph0
+-/
 
 variable (K V)
 
+#print IsNoetherian.rank_lt_aleph0 /-
 /-- The dimension of a noetherian module over a division ring, as a cardinal,
 is strictly less than the first infinite cardinal `ℵ₀`. -/
 theorem rank_lt_aleph0 : ∀ [IsNoetherian K V], Module.rank K V < ℵ₀ :=
   IsNoetherian.iff_rank_lt_aleph0.1
 #align is_noetherian.rank_lt_aleph_0 IsNoetherian.rank_lt_aleph0
+-/
 
 variable {K V}
 

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

@@ -30,12 +30,6 @@ namespace IsNoetherian
 
 variable {K : Type u} {V : Type v} [DivisionRing K] [AddCommGroup V] [Module K V]
 
-/- warning: is_noetherian.iff_rank_lt_aleph_0 -> IsNoetherian.iff_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)], Iff (IsNoetherian.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _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})) (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})
-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)], Iff (IsNoetherian.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _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})) (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})
-Case conversion may be inaccurate. Consider using '#align is_noetherian.iff_rank_lt_aleph_0 IsNoetherian.iff_rank_lt_aleph0ₓ'. -/
 /-- A module over a division ring is noetherian if and only if
 its dimension (as a cardinal) is strictly less than the first infinite cardinal `ℵ₀`.
 -/
@@ -56,12 +50,6 @@ theorem iff_rank_lt_aleph0 : IsNoetherian K V ↔ Module.rank K V < ℵ₀ :=
 
 variable (K V)
 
-/- warning: is_noetherian.rank_lt_aleph_0 -> IsNoetherian.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)] [_inst_4 : IsNoetherian.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _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})) (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}
-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)] [_inst_4 : IsNoetherian.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _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})) (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}
-Case conversion may be inaccurate. Consider using '#align is_noetherian.rank_lt_aleph_0 IsNoetherian.rank_lt_aleph0ₓ'. -/
 /-- The dimension of a noetherian module over a division ring, as a cardinal,
 is strictly less than the first infinite cardinal `ℵ₀`. -/
 theorem rank_lt_aleph0 : ∀ [IsNoetherian K V], Module.rank K V < ℵ₀ :=
@@ -82,12 +70,6 @@ noncomputable def fintypeBasisIndex {ι : Type _} [IsNoetherian K V] (b : Basis
 noncomputable instance [IsNoetherian K V] : Fintype (Basis.ofVectorSpaceIndex K V) :=
   fintypeBasisIndex (Basis.ofVectorSpace K V)
 
-/- warning: is_noetherian.finite_basis_index -> IsNoetherian.finite_basis_index 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)] {ι : Type.{u3}} {s : Set.{u3} ι} [_inst_4 : IsNoetherian.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3], (Basis.{u3, u1, u2} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) -> (Set.Finite.{u3} ι s)
-but is expected to have type
-  forall {K : Type.{u2}} {V : Type.{u3}} [_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)] {ι : Type.{u1}} {s : Set.{u1} ι} [_inst_4 : IsNoetherian.{u2, u3} K V (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3], (Basis.{u1, u2, u3} (Set.Elem.{u1} ι s) K V (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) -> (Set.Finite.{u1} ι s)
-Case conversion may be inaccurate. Consider using '#align is_noetherian.finite_basis_index IsNoetherian.finite_basis_indexₓ'. -/
 /-- In a noetherian module over a division ring,
 if a basis is indexed by a set, that set is finite. -/
 theorem finite_basis_index {ι : Type _} {s : Set ι} [IsNoetherian K V] (b : Basis s K V) :

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

@@ -148,10 +148,7 @@ theorem iff_fg : IsNoetherian K V ↔ Module.Finite K V :=
   by
   constructor
   · intro h
-    exact
-      ⟨⟨finset_basis_index K V, by
-          convert(finset_basis K V).span_eq
-          simp⟩⟩
+    exact ⟨⟨finset_basis_index K V, by convert(finset_basis K V).span_eq; simp⟩⟩
   · rintro ⟨s, hs⟩
     rw [IsNoetherian.iff_rank_lt_aleph0, ← rank_top, ← hs]
     exact lt_of_le_of_lt (rank_span_le _) s.finite_to_set.lt_aleph_0

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

@@ -30,7 +30,12 @@ namespace IsNoetherian
 
 variable {K : Type u} {V : Type v} [DivisionRing K] [AddCommGroup V] [Module K V]
 
-#print IsNoetherian.iff_rank_lt_aleph0 /-
+/- warning: is_noetherian.iff_rank_lt_aleph_0 -> IsNoetherian.iff_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)], Iff (IsNoetherian.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _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})) (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})
+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)], Iff (IsNoetherian.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _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})) (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})
+Case conversion may be inaccurate. Consider using '#align is_noetherian.iff_rank_lt_aleph_0 IsNoetherian.iff_rank_lt_aleph0ₓ'. -/
 /-- A module over a division ring is noetherian if and only if
 its dimension (as a cardinal) is strictly less than the first infinite cardinal `ℵ₀`.
 -/
@@ -48,17 +53,20 @@ theorem iff_rank_lt_aleph0 : IsNoetherian K V ↔ Module.rank K V < ℵ₀ :=
     refine' isNoetherian_of_fg_of_noetherian _ ⟨Set.Finite.toFinset hbfinite, _⟩
     rw [Set.Finite.coe_toFinset, ← b.span_eq, Basis.coe_ofVectorSpace, Subtype.range_coe]
 #align is_noetherian.iff_rank_lt_aleph_0 IsNoetherian.iff_rank_lt_aleph0
--/
 
 variable (K V)
 
-#print IsNoetherian.rank_lt_aleph0 /-
+/- warning: is_noetherian.rank_lt_aleph_0 -> IsNoetherian.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)] [_inst_4 : IsNoetherian.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _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})) (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}
+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)] [_inst_4 : IsNoetherian.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (DivisionRing.toDivisionSemiring.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _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})) (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}
+Case conversion may be inaccurate. Consider using '#align is_noetherian.rank_lt_aleph_0 IsNoetherian.rank_lt_aleph0ₓ'. -/
 /-- The dimension of a noetherian module over a division ring, as a cardinal,
 is strictly less than the first infinite cardinal `ℵ₀`. -/
 theorem rank_lt_aleph0 : ∀ [IsNoetherian K V], Module.rank K V < ℵ₀ :=
   IsNoetherian.iff_rank_lt_aleph0.1
 #align is_noetherian.rank_lt_aleph_0 IsNoetherian.rank_lt_aleph0
--/
 
 variable {K V}
 

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: Chris Hughes
 
 ! This file was ported from Lean 3 source module field_theory.finiteness
-! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
+! leanprover-community/mathlib commit 25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.LinearAlgebra.Dimension
 /-!
 # A module over a division ring is noetherian if and only if it is finite.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 -/
 
 

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

@@ -27,6 +27,7 @@ namespace IsNoetherian
 
 variable {K : Type u} {V : Type v} [DivisionRing K] [AddCommGroup V] [Module K V]
 
+#print IsNoetherian.iff_rank_lt_aleph0 /-
 /-- A module over a division ring is noetherian if and only if
 its dimension (as a cardinal) is strictly less than the first infinite cardinal `ℵ₀`.
 -/
@@ -44,27 +45,38 @@ theorem iff_rank_lt_aleph0 : IsNoetherian K V ↔ Module.rank K V < ℵ₀ :=
     refine' isNoetherian_of_fg_of_noetherian _ ⟨Set.Finite.toFinset hbfinite, _⟩
     rw [Set.Finite.coe_toFinset, ← b.span_eq, Basis.coe_ofVectorSpace, Subtype.range_coe]
 #align is_noetherian.iff_rank_lt_aleph_0 IsNoetherian.iff_rank_lt_aleph0
+-/
 
 variable (K V)
 
+#print IsNoetherian.rank_lt_aleph0 /-
 /-- The dimension of a noetherian module over a division ring, as a cardinal,
 is strictly less than the first infinite cardinal `ℵ₀`. -/
 theorem rank_lt_aleph0 : ∀ [IsNoetherian K V], Module.rank K V < ℵ₀ :=
   IsNoetherian.iff_rank_lt_aleph0.1
 #align is_noetherian.rank_lt_aleph_0 IsNoetherian.rank_lt_aleph0
+-/
 
 variable {K V}
 
+#print IsNoetherian.fintypeBasisIndex /-
 /-- In a noetherian module over a division ring, all bases are indexed by a finite type. -/
 noncomputable def fintypeBasisIndex {ι : Type _} [IsNoetherian K V] (b : Basis ι K V) : Fintype ι :=
   b.fintypeIndexOfRankLtAleph0 (rank_lt_aleph0 K V)
 #align is_noetherian.fintype_basis_index IsNoetherian.fintypeBasisIndex
+-/
 
 /-- In a noetherian module over a division ring,
 `basis.of_vector_space` is indexed by a finite type. -/
 noncomputable instance [IsNoetherian K V] : Fintype (Basis.ofVectorSpaceIndex K V) :=
   fintypeBasisIndex (Basis.ofVectorSpace K V)
 
+/- warning: is_noetherian.finite_basis_index -> IsNoetherian.finite_basis_index 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)] {ι : Type.{u3}} {s : Set.{u3} ι} [_inst_4 : IsNoetherian.{u1, u2} K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3], (Basis.{u3, u1, u2} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} ι) Type.{u3} (Set.hasCoeToSort.{u3} ι) s) K V (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) -> (Set.Finite.{u3} ι s)
+but is expected to have type
+  forall {K : Type.{u2}} {V : Type.{u3}} [_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)] {ι : Type.{u1}} {s : Set.{u1} ι} [_inst_4 : IsNoetherian.{u2, u3} K V (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3], (Basis.{u1, u2, u3} (Set.Elem.{u1} ι s) K V (DivisionSemiring.toSemiring.{u2} K (DivisionRing.toDivisionSemiring.{u2} K _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) -> (Set.Finite.{u1} ι s)
+Case conversion may be inaccurate. Consider using '#align is_noetherian.finite_basis_index IsNoetherian.finite_basis_indexₓ'. -/
 /-- In a noetherian module over a division ring,
 if a basis is indexed by a set, that set is finite. -/
 theorem finite_basis_index {ι : Type _} {s : Set ι} [IsNoetherian K V] (b : Basis s K V) :
@@ -74,24 +86,31 @@ theorem finite_basis_index {ι : Type _} {s : Set ι} [IsNoetherian K V] (b : Ba
 
 variable (K V)
 
+#print IsNoetherian.finsetBasisIndex /-
 /-- In a noetherian module over a division ring,
 there exists a finite basis. This is the indexing `finset`. -/
 noncomputable def finsetBasisIndex [IsNoetherian K V] : Finset V :=
   (finite_basis_index (Basis.ofVectorSpace K V)).toFinset
 #align is_noetherian.finset_basis_index IsNoetherian.finsetBasisIndex
+-/
 
+#print IsNoetherian.coe_finsetBasisIndex /-
 @[simp]
 theorem coe_finsetBasisIndex [IsNoetherian K V] :
     (↑(finsetBasisIndex K V) : Set V) = Basis.ofVectorSpaceIndex K V :=
   Set.Finite.coe_toFinset _
 #align is_noetherian.coe_finset_basis_index IsNoetherian.coe_finsetBasisIndex
+-/
 
+#print IsNoetherian.coeSort_finsetBasisIndex /-
 @[simp]
 theorem coeSort_finsetBasisIndex [IsNoetherian K V] :
     (finsetBasisIndex K V : Type _) = Basis.ofVectorSpaceIndex K V :=
   Set.Finite.coeSort_toFinset _
 #align is_noetherian.coe_sort_finset_basis_index IsNoetherian.coeSort_finsetBasisIndex
+-/
 
+#print IsNoetherian.finsetBasis /-
 /-- In a noetherian module over a division ring, there exists a finite basis.
 This is indexed by the `finset` `finite_dimensional.finset_basis_index`.
 This is in contrast to the result `finite_basis_index (basis.of_vector_space K V)`,
@@ -100,15 +119,19 @@ which provides a set and a `set.finite`.
 noncomputable def finsetBasis [IsNoetherian K V] : Basis (finsetBasisIndex K V) K V :=
   (Basis.ofVectorSpace K V).reindex (by simp)
 #align is_noetherian.finset_basis IsNoetherian.finsetBasis
+-/
 
+#print IsNoetherian.range_finsetBasis /-
 @[simp]
 theorem range_finsetBasis [IsNoetherian K V] :
     Set.range (finsetBasis K V) = Basis.ofVectorSpaceIndex K V := by
   rw [finset_basis, Basis.range_reindex, Basis.range_ofVectorSpace]
 #align is_noetherian.range_finset_basis IsNoetherian.range_finsetBasis
+-/
 
 variable {K V}
 
+#print IsNoetherian.iff_fg /-
 /-- A module over a division ring is noetherian if and only if it is finitely generated. -/
 theorem iff_fg : IsNoetherian K V ↔ Module.Finite K V :=
   by
@@ -122,6 +145,7 @@ theorem iff_fg : IsNoetherian K V ↔ Module.Finite K V :=
     rw [IsNoetherian.iff_rank_lt_aleph0, ← rank_top, ← hs]
     exact lt_of_le_of_lt (rank_span_le _) s.finite_to_set.lt_aleph_0
 #align is_noetherian.iff_fg IsNoetherian.iff_fg
+-/
 
 end IsNoetherian
 

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: Chris Hughes
 
 ! This file was ported from Lean 3 source module field_theory.finiteness
-! leanprover-community/mathlib commit 6eeb941cf39066417a09b1bbc6e74761cadfcb1a
+! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -30,10 +30,10 @@ variable {K : Type u} {V : Type v} [DivisionRing K] [AddCommGroup V] [Module K V
 /-- A module over a division ring is noetherian if and only if
 its dimension (as a cardinal) is strictly less than the first infinite cardinal `ℵ₀`.
 -/
-theorem iff_dim_lt_aleph0 : IsNoetherian K V ↔ Module.rank K V < ℵ₀ :=
+theorem iff_rank_lt_aleph0 : IsNoetherian K V ↔ Module.rank K V < ℵ₀ :=
   by
   let b := Basis.ofVectorSpace K V
-  rw [← b.mk_eq_dim'', lt_aleph_0_iff_set_finite]
+  rw [← b.mk_eq_rank'', lt_aleph_0_iff_set_finite]
   constructor
   · intro
     exact finite_of_linearIndependent (Basis.ofVectorSpaceIndex.linearIndependent K V)
@@ -43,21 +43,21 @@ theorem iff_dim_lt_aleph0 : IsNoetherian K V ↔ Module.rank K V < ℵ₀ :=
         (id _)
     refine' isNoetherian_of_fg_of_noetherian _ ⟨Set.Finite.toFinset hbfinite, _⟩
     rw [Set.Finite.coe_toFinset, ← b.span_eq, Basis.coe_ofVectorSpace, Subtype.range_coe]
-#align is_noetherian.iff_dim_lt_aleph_0 IsNoetherian.iff_dim_lt_aleph0
+#align is_noetherian.iff_rank_lt_aleph_0 IsNoetherian.iff_rank_lt_aleph0
 
 variable (K V)
 
 /-- The dimension of a noetherian module over a division ring, as a cardinal,
 is strictly less than the first infinite cardinal `ℵ₀`. -/
-theorem dim_lt_aleph0 : ∀ [IsNoetherian K V], Module.rank K V < ℵ₀ :=
-  IsNoetherian.iff_dim_lt_aleph0.1
-#align is_noetherian.dim_lt_aleph_0 IsNoetherian.dim_lt_aleph0
+theorem rank_lt_aleph0 : ∀ [IsNoetherian K V], Module.rank K V < ℵ₀ :=
+  IsNoetherian.iff_rank_lt_aleph0.1
+#align is_noetherian.rank_lt_aleph_0 IsNoetherian.rank_lt_aleph0
 
 variable {K V}
 
 /-- In a noetherian module over a division ring, all bases are indexed by a finite type. -/
 noncomputable def fintypeBasisIndex {ι : Type _} [IsNoetherian K V] (b : Basis ι K V) : Fintype ι :=
-  b.fintypeIndexOfDimLtAleph0 (dim_lt_aleph0 K V)
+  b.fintypeIndexOfRankLtAleph0 (rank_lt_aleph0 K V)
 #align is_noetherian.fintype_basis_index IsNoetherian.fintypeBasisIndex
 
 /-- In a noetherian module over a division ring,
@@ -69,7 +69,7 @@ noncomputable instance [IsNoetherian K V] : Fintype (Basis.ofVectorSpaceIndex K
 if a basis is indexed by a set, that set is finite. -/
 theorem finite_basis_index {ι : Type _} {s : Set ι} [IsNoetherian K V] (b : Basis s K V) :
     s.Finite :=
-  b.finite_index_of_dim_lt_aleph0 (dim_lt_aleph0 K V)
+  b.finite_index_of_rank_lt_aleph0 (rank_lt_aleph0 K V)
 #align is_noetherian.finite_basis_index IsNoetherian.finite_basis_index
 
 variable (K V)
@@ -119,8 +119,8 @@ theorem iff_fg : IsNoetherian K V ↔ Module.Finite K V :=
           convert(finset_basis K V).span_eq
           simp⟩⟩
   · rintro ⟨s, hs⟩
-    rw [IsNoetherian.iff_dim_lt_aleph0, ← dim_top, ← hs]
-    exact lt_of_le_of_lt (dim_span_le _) s.finite_to_set.lt_aleph_0
+    rw [IsNoetherian.iff_rank_lt_aleph0, ← rank_top, ← hs]
+    exact lt_of_le_of_lt (rank_span_le _) s.finite_to_set.lt_aleph_0
 #align is_noetherian.iff_fg IsNoetherian.iff_fg
 
 end IsNoetherian

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

@@ -116,7 +116,7 @@ theorem iff_fg : IsNoetherian K V ↔ Module.Finite K V :=
   · intro h
     exact
       ⟨⟨finset_basis_index K V, by
-          convert (finset_basis K V).span_eq
+          convert(finset_basis K V).span_eq
           simp⟩⟩
   · rintro ⟨s, hs⟩
     rw [IsNoetherian.iff_dim_lt_aleph0, ← dim_top, ← hs]

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

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -17,7 +17,8 @@ import Mathlib.LinearAlgebra.Dimension.Finite
 
 universe u v
 
-open Classical Cardinal
+open scoped Classical
+open Cardinal
 
 open Cardinal Submodule Module Function
 

@@ -87,7 +87,7 @@ theorem coeSort_finsetBasisIndex [IsNoetherian K V] :
 #align is_noetherian.coe_sort_finset_basis_index IsNoetherian.coeSort_finsetBasisIndex
 
 /-- In a noetherian module over a division ring, there exists a finite basis.
-This is indexed by the `Finset` `FiniteDimensional.finsetBasisIndex`.
+This is indexed by the `Finset` `IsNoetherian.finsetBasisIndex`.
 This is in contrast to the result `finite_basis_index (Basis.ofVectorSpace K V)`,
 which provides a set and a `Set.finite`.
 -/

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 +3,9 @@ Copyright (c) 2019 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Mathlib.LinearAlgebra.Dimension.DivisionRing
+import Mathlib.LinearAlgebra.Basis.VectorSpace
+import Mathlib.LinearAlgebra.Dimension.Constructions
+import Mathlib.LinearAlgebra.Dimension.Finite
 
 #align_import field_theory.finiteness from "leanprover-community/mathlib"@"039a089d2a4b93c761b234f3e5f5aeb752bac60f"
 

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>

@@ -3,8 +3,7 @@ Copyright (c) 2019 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Mathlib.RingTheory.Finiteness
-import Mathlib.LinearAlgebra.Dimension
+import Mathlib.LinearAlgebra.Dimension.DivisionRing
 
 #align_import field_theory.finiteness from "leanprover-community/mathlib"@"039a089d2a4b93c761b234f3e5f5aeb752bac60f"
 
@@ -43,11 +42,8 @@ theorem iff_rank_lt_aleph0 : IsNoetherian K V ↔ Module.rank K V < ℵ₀ := by
 
 variable (K V)
 
-/-- The dimension of a noetherian module over a division ring, as a cardinal,
-is strictly less than the first infinite cardinal `ℵ₀`. -/
-theorem rank_lt_aleph0 : ∀ [IsNoetherian K V], Module.rank K V < ℵ₀ :=
-  @IsNoetherian.iff_rank_lt_aleph0.1
-#align is_noetherian.rank_lt_aleph_0 IsNoetherian.rank_lt_aleph0
+@[deprecated] protected alias rank_lt_aleph0 := _root_.rank_lt_aleph0
+#align is_noetherian.rank_lt_aleph_0 rank_lt_aleph0
 
 variable {K V}
 

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

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

@@ -32,7 +32,7 @@ theorem iff_rank_lt_aleph0 : IsNoetherian K V ↔ Module.rank K V < ℵ₀ := by
   rw [← b.mk_eq_rank'', lt_aleph0_iff_set_finite]
   constructor
   · intro
-    exact finite_of_linearIndependent (Basis.ofVectorSpaceIndex.linearIndependent K V)
+    exact (Basis.ofVectorSpaceIndex.linearIndependent K V).set_finite_of_isNoetherian
   · intro hbfinite
     refine'
       @isNoetherian_of_linearEquiv K (⊤ : Submodule K V) V _ _ _ _ _ (LinearEquiv.ofTop _ rfl)

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

This has nice performance benefits.

@@ -52,7 +52,7 @@ theorem rank_lt_aleph0 : ∀ [IsNoetherian K V], Module.rank K V < ℵ₀ :=
 variable {K V}
 
 /-- In a noetherian module over a division ring, all bases are indexed by a finite type. -/
-noncomputable def fintypeBasisIndex {ι : Type _} [IsNoetherian K V] (b : Basis ι K V) : Fintype ι :=
+noncomputable def fintypeBasisIndex {ι : Type*} [IsNoetherian K V] (b : Basis ι K V) : Fintype ι :=
   b.fintypeIndexOfRankLtAleph0 (rank_lt_aleph0 K V)
 #align is_noetherian.fintype_basis_index IsNoetherian.fintypeBasisIndex
 
@@ -63,7 +63,7 @@ noncomputable instance [IsNoetherian K V] : Fintype (Basis.ofVectorSpaceIndex K
 
 /-- In a noetherian module over a division ring,
 if a basis is indexed by a set, that set is finite. -/
-theorem finite_basis_index {ι : Type _} {s : Set ι} [IsNoetherian K V] (b : Basis s K V) :
+theorem finite_basis_index {ι : Type*} {s : Set ι} [IsNoetherian K V] (b : Basis s K V) :
     s.Finite :=
   b.finite_index_of_rank_lt_aleph0 (rank_lt_aleph0 K V)
 #align is_noetherian.finite_basis_index IsNoetherian.finite_basis_index

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module field_theory.finiteness
-! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.Finiteness
 import Mathlib.LinearAlgebra.Dimension
 
+#align_import field_theory.finiteness from "leanprover-community/mathlib"@"039a089d2a4b93c761b234f3e5f5aeb752bac60f"
+
 /-!
 # A module over a division ring is noetherian if and only if it is finite.
 

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