algebra.direct_sum.decomposition | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

4e861f25

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

33c67ae6

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2022 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Jujian Zhang
 -/
-import Mathbin.Algebra.DirectSum.Module
-import Mathbin.Algebra.Module.Submodule.Basic
+import Algebra.DirectSum.Module
+import Algebra.Module.Submodule.Basic
 
 #align_import algebra.direct_sum.decomposition from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"

33c67ae6

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Jujian Zhang
-
-! This file was ported from Lean 3 source module algebra.direct_sum.decomposition
-! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.DirectSum.Module
 import Mathbin.Algebra.Module.Submodule.Basic
 
+#align_import algebra.direct_sum.decomposition from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
+
 /-!
 # Decompositions of additive monoids, groups, and modules into direct sums

33c67ae6

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -63,8 +63,6 @@ class Decomposition where
 #align direct_sum.decomposition DirectSum.Decomposition
 -/
 
-include M
-
 /-- `direct_sum.decomposition` instances, while carrying data, are always equal. -/
 instance : Subsingleton (Decomposition ℳ) :=
   ⟨fun x y => by
@@ -75,9 +73,11 @@ instance : Subsingleton (Decomposition ℳ) :=
 
 variable [Decomposition ℳ]
 
+#print DirectSum.Decomposition.isInternal /-
 protected theorem Decomposition.isInternal : DirectSum.IsInternal ℳ :=
   ⟨Decomposition.right_inv.Injective, Decomposition.left_inv.Surjective⟩
 #align direct_sum.decomposition.is_internal DirectSum.Decomposition.isInternal
+-/
 
 #print DirectSum.decompose /-
 /-- If `M` is graded by `ι` with degree `i` component `ℳ i`, then it is isomorphic as
@@ -90,6 +90,7 @@ def decompose : M ≃ ⨁ i, ℳ i where
 #align direct_sum.decompose DirectSum.decompose
 -/
 
+#print DirectSum.Decomposition.inductionOn /-
 protected theorem Decomposition.inductionOn {p : M → Prop} (h_zero : p 0)
     (h_homogeneous : ∀ {i} (m : ℳ i), p (m : M)) (h_add : ∀ m m' : M, p m → p m' → p (m + m')) :
     ∀ m, p m :=
@@ -105,76 +106,104 @@ protected theorem Decomposition.inductionOn {p : M → Prop} (h_zero : p 0)
   exact fun m =>
     AddSubmonoid.iSup_induction ℳ' (mem m) (fun i m h => h_homogeneous ⟨m, h⟩) h_zero h_add
 #align direct_sum.decomposition.induction_on DirectSum.Decomposition.inductionOn
+-/
 
+#print DirectSum.Decomposition.decompose'_eq /-
 @[simp]
 theorem Decomposition.decompose'_eq : Decomposition.decompose' = decompose ℳ :=
   rfl
 #align direct_sum.decomposition.decompose'_eq DirectSum.Decomposition.decompose'_eq
+-/
 
+#print DirectSum.decompose_symm_of /-
 @[simp]
 theorem decompose_symm_of {i : ι} (x : ℳ i) : (decompose ℳ).symm (DirectSum.of _ i x) = x :=
   DirectSum.coeAddMonoidHom_of ℳ _ _
 #align direct_sum.decompose_symm_of DirectSum.decompose_symm_of
+-/
 
+#print DirectSum.decompose_coe /-
 @[simp]
 theorem decompose_coe {i : ι} (x : ℳ i) : decompose ℳ (x : M) = DirectSum.of _ i x := by
   rw [← decompose_symm_of, Equiv.apply_symm_apply]
 #align direct_sum.decompose_coe DirectSum.decompose_coe
+-/
 
+#print DirectSum.decompose_of_mem /-
 theorem decompose_of_mem {x : M} {i : ι} (hx : x ∈ ℳ i) :
     decompose ℳ x = DirectSum.of (fun i => ℳ i) i ⟨x, hx⟩ :=
   decompose_coe _ ⟨x, hx⟩
 #align direct_sum.decompose_of_mem DirectSum.decompose_of_mem
+-/
 
+#print DirectSum.decompose_of_mem_same /-
 theorem decompose_of_mem_same {x : M} {i : ι} (hx : x ∈ ℳ i) : (decompose ℳ x i : M) = x := by
   rw [decompose_of_mem _ hx, DirectSum.of_eq_same, Subtype.coe_mk]
 #align direct_sum.decompose_of_mem_same DirectSum.decompose_of_mem_same
+-/
 
+#print DirectSum.decompose_of_mem_ne /-
 theorem decompose_of_mem_ne {x : M} {i j : ι} (hx : x ∈ ℳ i) (hij : i ≠ j) :
     (decompose ℳ x j : M) = 0 := by
   rw [decompose_of_mem _ hx, DirectSum.of_eq_of_ne _ _ _ _ hij, ZeroMemClass.coe_zero]
 #align direct_sum.decompose_of_mem_ne DirectSum.decompose_of_mem_ne
+-/
 
+#print DirectSum.decomposeAddEquiv /-
 /-- If `M` is graded by `ι` with degree `i` component `ℳ i`, then it is isomorphic as
 an additive monoid to a direct sum of components. -/
 @[simps (config := { fullyApplied := false })]
 def decomposeAddEquiv : M ≃+ ⨁ i, ℳ i :=
   AddEquiv.symm { (decompose ℳ).symm with map_add' := map_add (DirectSum.coeAddMonoidHom ℳ) }
 #align direct_sum.decompose_add_equiv DirectSum.decomposeAddEquiv
+-/
 
+#print DirectSum.decompose_zero /-
 @[simp]
 theorem decompose_zero : decompose ℳ (0 : M) = 0 :=
   map_zero (decomposeAddEquiv ℳ)
 #align direct_sum.decompose_zero DirectSum.decompose_zero
+-/
 
+#print DirectSum.decompose_symm_zero /-
 @[simp]
 theorem decompose_symm_zero : (decompose ℳ).symm 0 = (0 : M) :=
   map_zero (decomposeAddEquiv ℳ).symm
 #align direct_sum.decompose_symm_zero DirectSum.decompose_symm_zero
+-/
 
+#print DirectSum.decompose_add /-
 @[simp]
 theorem decompose_add (x y : M) : decompose ℳ (x + y) = decompose ℳ x + decompose ℳ y :=
   map_add (decomposeAddEquiv ℳ) x y
 #align direct_sum.decompose_add DirectSum.decompose_add
+-/
 
+#print DirectSum.decompose_symm_add /-
 @[simp]
 theorem decompose_symm_add (x y : ⨁ i, ℳ i) :
     (decompose ℳ).symm (x + y) = (decompose ℳ).symm x + (decompose ℳ).symm y :=
   map_add (decomposeAddEquiv ℳ).symm x y
 #align direct_sum.decompose_symm_add DirectSum.decompose_symm_add
+-/
 
+#print DirectSum.decompose_sum /-
 @[simp]
 theorem decompose_sum {ι'} (s : Finset ι') (f : ι' → M) :
     decompose ℳ (∑ i in s, f i) = ∑ i in s, decompose ℳ (f i) :=
   map_sum (decomposeAddEquiv ℳ) f s
 #align direct_sum.decompose_sum DirectSum.decompose_sum
+-/
 
+#print DirectSum.decompose_symm_sum /-
 @[simp]
 theorem decompose_symm_sum {ι'} (s : Finset ι') (f : ι' → ⨁ i, ℳ i) :
     (decompose ℳ).symm (∑ i in s, f i) = ∑ i in s, (decompose ℳ).symm (f i) :=
   map_sum (decomposeAddEquiv ℳ).symm f s
 #align direct_sum.decompose_symm_sum DirectSum.decompose_symm_sum
+-/
 
+#print DirectSum.sum_support_decompose /-
 theorem sum_support_decompose [∀ (i) (x : ℳ i), Decidable (x ≠ 0)] (r : M) :
     ∑ i in (decompose ℳ r).support, (decompose ℳ r i : M) = r :=
   by
@@ -183,6 +212,7 @@ theorem sum_support_decompose [∀ (i) (x : ℳ i), Decidable (x ≠ 0)] (r : M)
   rw [decompose_symm_sum]
   simp_rw [decompose_symm_of]
 #align direct_sum.sum_support_decompose DirectSum.sum_support_decompose
+-/
 
 end AddCommMonoid
 
@@ -206,28 +236,34 @@ variable [SetLike σ M] [AddSubgroupClass σ M] (ℳ : ι → σ)
 
 variable [Decomposition ℳ]
 
-include M
-
+#print DirectSum.decompose_neg /-
 @[simp]
 theorem decompose_neg (x : M) : decompose ℳ (-x) = -decompose ℳ x :=
   map_neg (decomposeAddEquiv ℳ) x
 #align direct_sum.decompose_neg DirectSum.decompose_neg
+-/
 
+#print DirectSum.decompose_symm_neg /-
 @[simp]
 theorem decompose_symm_neg (x : ⨁ i, ℳ i) : (decompose ℳ).symm (-x) = -(decompose ℳ).symm x :=
   map_neg (decomposeAddEquiv ℳ).symm x
 #align direct_sum.decompose_symm_neg DirectSum.decompose_symm_neg
+-/
 
+#print DirectSum.decompose_sub /-
 @[simp]
 theorem decompose_sub (x y : M) : decompose ℳ (x - y) = decompose ℳ x - decompose ℳ y :=
   map_sub (decomposeAddEquiv ℳ) x y
 #align direct_sum.decompose_sub DirectSum.decompose_sub
+-/
 
+#print DirectSum.decompose_symm_sub /-
 @[simp]
 theorem decompose_symm_sub (x y : ⨁ i, ℳ i) :
     (decompose ℳ).symm (x - y) = (decompose ℳ).symm x - (decompose ℳ).symm y :=
   map_sub (decomposeAddEquiv ℳ).symm x y
 #align direct_sum.decompose_symm_sub DirectSum.decompose_symm_sub
+-/
 
 end AddCommGroup
 
@@ -239,8 +275,6 @@ variable (ℳ : ι → Submodule R M)
 
 variable [Decomposition ℳ]
 
-include M
-
 #print DirectSum.decomposeLinearEquiv /-
 /-- If `M` is graded by `ι` with degree `i` component `ℳ i`, then it is isomorphic as
 a module to a direct sum of components. -/
@@ -251,10 +285,12 @@ def decomposeLinearEquiv : M ≃ₗ[R] ⨁ i, ℳ i :=
 #align direct_sum.decompose_linear_equiv DirectSum.decomposeLinearEquiv
 -/
 
+#print DirectSum.decompose_smul /-
 @[simp]
 theorem decompose_smul (r : R) (x : M) : decompose ℳ (r • x) = r • decompose ℳ x :=
   map_smul (decomposeLinearEquiv ℳ) r x
 #align direct_sum.decompose_smul DirectSum.decompose_smul
+-/
 
 end Module

33c67ae6

bump to nightly-2023-06-10-07

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

3fdc57bc

Diff

@@ -176,7 +176,7 @@ theorem decompose_symm_sum {ι'} (s : Finset ι') (f : ι' → ⨁ i, ℳ i) :
 #align direct_sum.decompose_symm_sum DirectSum.decompose_symm_sum
 
 theorem sum_support_decompose [∀ (i) (x : ℳ i), Decidable (x ≠ 0)] (r : M) :
-    (∑ i in (decompose ℳ r).support, (decompose ℳ r i : M)) = r :=
+    ∑ i in (decompose ℳ r).support, (decompose ℳ r i : M) = r :=
   by
   conv_rhs =>
     rw [← (decompose ℳ).symm_apply_apply r, ← sum_support_of (fun i => ℳ i) (decompose ℳ r)]

33c67ae6

bump to nightly-2023-06-08-13

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

f6099bb9

Diff

@@ -241,6 +241,7 @@ variable [Decomposition ℳ]
 
 include M
 
+#print DirectSum.decomposeLinearEquiv /-
 /-- If `M` is graded by `ι` with degree `i` component `ℳ i`, then it is isomorphic as
 a module to a direct sum of components. -/
 @[simps (config := { fullyApplied := false })]
@@ -248,6 +249,7 @@ def decomposeLinearEquiv : M ≃ₗ[R] ⨁ i, ℳ i :=
   LinearEquiv.symm
     { (decomposeAddEquiv ℳ).symm with map_smul' := map_smul (DirectSum.coeLinearMap ℳ) }
 #align direct_sum.decompose_linear_equiv DirectSum.decomposeLinearEquiv
+-/
 
 @[simp]
 theorem decompose_smul (r : R) (x : M) : decompose ℳ (r • x) = r • decompose ℳ x :=

33c67ae6

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -39,7 +39,7 @@ bundled homs, but means we don't have to repeat statements for different types o
 
 variable {ι R M σ : Type _}
 
-open DirectSum BigOperators
+open scoped DirectSum BigOperators
 
 namespace DirectSum

33c67ae6

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -75,12 +75,6 @@ instance : Subsingleton (Decomposition ℳ) :=
 
 variable [Decomposition ℳ]
 
-/- warning: direct_sum.decomposition.is_internal -> DirectSum.Decomposition.isInternal is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {M : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : SetLike.{u3, u2} σ M] [_inst_4 : AddSubmonoidClass.{u3, u2} σ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u1, u2, u3} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ], DirectSum.IsInternal.{u1, u2, u3} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ
-but is expected to have type
-  forall {ι : Type.{u3}} {M : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : SetLike.{u1, u2} σ M] [_inst_4 : AddSubmonoidClass.{u1, u2} σ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ], DirectSum.IsInternal.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ
-Case conversion may be inaccurate. Consider using '#align direct_sum.decomposition.is_internal DirectSum.Decomposition.isInternalₓ'. -/
 protected theorem Decomposition.isInternal : DirectSum.IsInternal ℳ :=
   ⟨Decomposition.right_inv.Injective, Decomposition.left_inv.Surjective⟩
 #align direct_sum.decomposition.is_internal DirectSum.Decomposition.isInternal
@@ -96,12 +90,6 @@ def decompose : M ≃ ⨁ i, ℳ i where
 #align direct_sum.decompose DirectSum.decompose
 -/
 
-/- warning: direct_sum.decomposition.induction_on -> DirectSum.Decomposition.inductionOn is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {M : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : SetLike.{u3, u2} σ M] [_inst_4 : AddSubmonoidClass.{u3, u2} σ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u1, u2, u3} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ] {p : M -> Prop}, (p (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))))) -> (forall {i : ι} (m : coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)), p ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) M (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u3} M σ (SetLike.hasMem.{u3, u2} σ M _inst_3) x (ℳ i)))))) m)) -> (forall (m : M) (m' : M), (p m) -> (p m') -> (p (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) m m'))) -> (forall (m : M), p m)
-but is expected to have type
-  forall {ι : Type.{u3}} {M : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : SetLike.{u1, u2} σ M] [_inst_4 : AddSubmonoidClass.{u1, u2} σ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ] {p : M -> Prop}, (p (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) -> (forall {i : ι} (m : Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))), p (Subtype.val.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Set.{u2} M) (Set.instMembershipSet.{u2} M) x (SetLike.coe.{u1, u2} σ M _inst_3 (ℳ i))) m)) -> (forall (m : M) (m' : M), (p m) -> (p m') -> (p (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) m m'))) -> (forall (m : M), p m)
-Case conversion may be inaccurate. Consider using '#align direct_sum.decomposition.induction_on DirectSum.Decomposition.inductionOnₓ'. -/
 protected theorem Decomposition.inductionOn {p : M → Prop} (h_zero : p 0)
     (h_homogeneous : ∀ {i} (m : ℳ i), p (m : M)) (h_add : ∀ m m' : M, p m → p m' → p (m + m')) :
     ∀ m, p m :=
@@ -118,62 +106,35 @@ protected theorem Decomposition.inductionOn {p : M → Prop} (h_zero : p 0)
     AddSubmonoid.iSup_induction ℳ' (mem m) (fun i m h => h_homogeneous ⟨m, h⟩) h_zero h_add
 #align direct_sum.decomposition.induction_on DirectSum.Decomposition.inductionOn
 
-/- warning: direct_sum.decomposition.decompose'_eq -> DirectSum.Decomposition.decompose'_eq is a dubious translation:
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 @[simp]
 theorem Decomposition.decompose'_eq : Decomposition.decompose' = decompose ℳ :=
   rfl
 #align direct_sum.decomposition.decompose'_eq DirectSum.Decomposition.decompose'_eq
 
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 @[simp]
 theorem decompose_symm_of {i : ι} (x : ℳ i) : (decompose ℳ).symm (DirectSum.of _ i x) = x :=
   DirectSum.coeAddMonoidHom_of ℳ _ _
 #align direct_sum.decompose_symm_of DirectSum.decompose_symm_of
 
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 @[simp]
 theorem decompose_coe {i : ι} (x : ℳ i) : decompose ℳ (x : M) = DirectSum.of _ i x := by
   rw [← decompose_symm_of, Equiv.apply_symm_apply]
 #align direct_sum.decompose_coe DirectSum.decompose_coe
 
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 theorem decompose_of_mem {x : M} {i : ι} (hx : x ∈ ℳ i) :
     decompose ℳ x = DirectSum.of (fun i => ℳ i) i ⟨x, hx⟩ :=
   decompose_coe _ ⟨x, hx⟩
 #align direct_sum.decompose_of_mem DirectSum.decompose_of_mem
 
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 theorem decompose_of_mem_same {x : M} {i : ι} (hx : x ∈ ℳ i) : (decompose ℳ x i : M) = x := by
   rw [decompose_of_mem _ hx, DirectSum.of_eq_same, Subtype.coe_mk]
 #align direct_sum.decompose_of_mem_same DirectSum.decompose_of_mem_same
 
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 theorem decompose_of_mem_ne {x : M} {i j : ι} (hx : x ∈ ℳ i) (hij : i ≠ j) :
     (decompose ℳ x j : M) = 0 := by
   rw [decompose_of_mem _ hx, DirectSum.of_eq_of_ne _ _ _ _ hij, ZeroMemClass.coe_zero]
 #align direct_sum.decompose_of_mem_ne DirectSum.decompose_of_mem_ne
 
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 /-- If `M` is graded by `ι` with degree `i` component `ℳ i`, then it is isomorphic as
 an additive monoid to a direct sum of components. -/
 @[simps (config := { fullyApplied := false })]
@@ -181,66 +142,39 @@ def decomposeAddEquiv : M ≃+ ⨁ i, ℳ i :=
   AddEquiv.symm { (decompose ℳ).symm with map_add' := map_add (DirectSum.coeAddMonoidHom ℳ) }
 #align direct_sum.decompose_add_equiv DirectSum.decomposeAddEquiv
 
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 @[simp]
 theorem decompose_zero : decompose ℳ (0 : M) = 0 :=
   map_zero (decomposeAddEquiv ℳ)
 #align direct_sum.decompose_zero DirectSum.decompose_zero
 
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 @[simp]
 theorem decompose_symm_zero : (decompose ℳ).symm 0 = (0 : M) :=
   map_zero (decomposeAddEquiv ℳ).symm
 #align direct_sum.decompose_symm_zero DirectSum.decompose_symm_zero
 
-/- warning: direct_sum.decompose_add -> DirectSum.decompose_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_add DirectSum.decompose_addₓ'. -/
 @[simp]
 theorem decompose_add (x y : M) : decompose ℳ (x + y) = decompose ℳ x + decompose ℳ y :=
   map_add (decomposeAddEquiv ℳ) x y
 #align direct_sum.decompose_add DirectSum.decompose_add
 
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 @[simp]
 theorem decompose_symm_add (x y : ⨁ i, ℳ i) :
     (decompose ℳ).symm (x + y) = (decompose ℳ).symm x + (decompose ℳ).symm y :=
   map_add (decomposeAddEquiv ℳ).symm x y
 #align direct_sum.decompose_symm_add DirectSum.decompose_symm_add
 
-/- warning: direct_sum.decompose_sum -> DirectSum.decompose_sum is a dubious translation:
-<too large>
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 @[simp]
 theorem decompose_sum {ι'} (s : Finset ι') (f : ι' → M) :
     decompose ℳ (∑ i in s, f i) = ∑ i in s, decompose ℳ (f i) :=
   map_sum (decomposeAddEquiv ℳ) f s
 #align direct_sum.decompose_sum DirectSum.decompose_sum
 
-/- warning: direct_sum.decompose_symm_sum -> DirectSum.decompose_symm_sum is a dubious translation:
-<too large>
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 @[simp]
 theorem decompose_symm_sum {ι'} (s : Finset ι') (f : ι' → ⨁ i, ℳ i) :
     (decompose ℳ).symm (∑ i in s, f i) = ∑ i in s, (decompose ℳ).symm (f i) :=
   map_sum (decomposeAddEquiv ℳ).symm f s
 #align direct_sum.decompose_symm_sum DirectSum.decompose_symm_sum
 
-/- warning: direct_sum.sum_support_decompose -> DirectSum.sum_support_decompose is a dubious translation:
-<too large>
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 theorem sum_support_decompose [∀ (i) (x : ℳ i), Decidable (x ≠ 0)] (r : M) :
     (∑ i in (decompose ℳ r).support, (decompose ℳ r i : M)) = r :=
   by
@@ -274,33 +208,21 @@ variable [Decomposition ℳ]
 
 include M
 
-/- warning: direct_sum.decompose_neg -> DirectSum.decompose_neg is a dubious translation:
-<too large>
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 @[simp]
 theorem decompose_neg (x : M) : decompose ℳ (-x) = -decompose ℳ x :=
   map_neg (decomposeAddEquiv ℳ) x
 #align direct_sum.decompose_neg DirectSum.decompose_neg
 
-/- warning: direct_sum.decompose_symm_neg -> DirectSum.decompose_symm_neg is a dubious translation:
-<too large>
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 @[simp]
 theorem decompose_symm_neg (x : ⨁ i, ℳ i) : (decompose ℳ).symm (-x) = -(decompose ℳ).symm x :=
   map_neg (decomposeAddEquiv ℳ).symm x
 #align direct_sum.decompose_symm_neg DirectSum.decompose_symm_neg
 
-/- warning: direct_sum.decompose_sub -> DirectSum.decompose_sub is a dubious translation:
-<too large>
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 @[simp]
 theorem decompose_sub (x y : M) : decompose ℳ (x - y) = decompose ℳ x - decompose ℳ y :=
   map_sub (decomposeAddEquiv ℳ) x y
 #align direct_sum.decompose_sub DirectSum.decompose_sub
 
-/- warning: direct_sum.decompose_symm_sub -> DirectSum.decompose_symm_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_sub DirectSum.decompose_symm_subₓ'. -/
 @[simp]
 theorem decompose_symm_sub (x y : ⨁ i, ℳ i) :
     (decompose ℳ).symm (x - y) = (decompose ℳ).symm x - (decompose ℳ).symm y :=
@@ -319,12 +241,6 @@ variable [Decomposition ℳ]
 
 include M
 
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 /-- If `M` is graded by `ι` with degree `i` component `ℳ i`, then it is isomorphic as
 a module to a direct sum of components. -/
 @[simps (config := { fullyApplied := false })]
@@ -333,9 +249,6 @@ def decomposeLinearEquiv : M ≃ₗ[R] ⨁ i, ℳ i :=
     { (decomposeAddEquiv ℳ).symm with map_smul' := map_smul (DirectSum.coeLinearMap ℳ) }
 #align direct_sum.decompose_linear_equiv DirectSum.decomposeLinearEquiv
 
-/- warning: direct_sum.decompose_smul -> DirectSum.decompose_smul is a dubious translation:
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 @[simp]
 theorem decompose_smul (r : R) (x : M) : decompose ℳ (r • x) = r • decompose ℳ x :=
   map_smul (decomposeLinearEquiv ℳ) r x

33c67ae6

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -130,10 +130,7 @@ theorem Decomposition.decompose'_eq : Decomposition.decompose' = decompose ℳ :
 #align direct_sum.decomposition.decompose'_eq DirectSum.Decomposition.decompose'_eq
 
 /- warning: direct_sum.decompose_symm_of -> DirectSum.decompose_symm_of is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_of DirectSum.decompose_symm_ofₓ'. -/
 @[simp]
 theorem decompose_symm_of {i : ι} (x : ℳ i) : (decompose ℳ).symm (DirectSum.of _ i x) = x :=
@@ -141,10 +138,7 @@ theorem decompose_symm_of {i : ι} (x : ℳ i) : (decompose ℳ).symm (DirectSum
 #align direct_sum.decompose_symm_of DirectSum.decompose_symm_of
 
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 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_coe DirectSum.decompose_coeₓ'. -/
 @[simp]
 theorem decompose_coe {i : ι} (x : ℳ i) : decompose ℳ (x : M) = DirectSum.of _ i x := by
@@ -152,10 +146,7 @@ theorem decompose_coe {i : ι} (x : ℳ i) : decompose ℳ (x : M) = DirectSum.o
 #align direct_sum.decompose_coe DirectSum.decompose_coe
 
 /- warning: direct_sum.decompose_of_mem -> DirectSum.decompose_of_mem is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_of_mem DirectSum.decompose_of_memₓ'. -/
 theorem decompose_of_mem {x : M} {i : ι} (hx : x ∈ ℳ i) :
     decompose ℳ x = DirectSum.of (fun i => ℳ i) i ⟨x, hx⟩ :=
@@ -163,20 +154,14 @@ theorem decompose_of_mem {x : M} {i : ι} (hx : x ∈ ℳ i) :
 #align direct_sum.decompose_of_mem DirectSum.decompose_of_mem
 
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 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_of_mem_same DirectSum.decompose_of_mem_sameₓ'. -/
 theorem decompose_of_mem_same {x : M} {i : ι} (hx : x ∈ ℳ i) : (decompose ℳ x i : M) = x := by
   rw [decompose_of_mem _ hx, DirectSum.of_eq_same, Subtype.coe_mk]
 #align direct_sum.decompose_of_mem_same DirectSum.decompose_of_mem_same
 
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 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_of_mem_ne DirectSum.decompose_of_mem_neₓ'. -/
 theorem decompose_of_mem_ne {x : M} {i j : ι} (hx : x ∈ ℳ i) (hij : i ≠ j) :
     (decompose ℳ x j : M) = 0 := by
@@ -219,10 +204,7 @@ theorem decompose_symm_zero : (decompose ℳ).symm 0 = (0 : M) :=
 #align direct_sum.decompose_symm_zero DirectSum.decompose_symm_zero
 
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 @[simp]
 theorem decompose_add (x y : M) : decompose ℳ (x + y) = decompose ℳ x + decompose ℳ y :=
@@ -230,10 +212,7 @@ theorem decompose_add (x y : M) : decompose ℳ (x + y) = decompose ℳ x + deco
 #align direct_sum.decompose_add DirectSum.decompose_add
 
 /- warning: direct_sum.decompose_symm_add -> DirectSum.decompose_symm_add is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_add DirectSum.decompose_symm_addₓ'. -/
 @[simp]
 theorem decompose_symm_add (x y : ⨁ i, ℳ i) :
@@ -242,10 +221,7 @@ theorem decompose_symm_add (x y : ⨁ i, ℳ i) :
 #align direct_sum.decompose_symm_add DirectSum.decompose_symm_add
 
 /- warning: direct_sum.decompose_sum -> DirectSum.decompose_sum is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_sum DirectSum.decompose_sumₓ'. -/
 @[simp]
 theorem decompose_sum {ι'} (s : Finset ι') (f : ι' → M) :
@@ -254,10 +230,7 @@ theorem decompose_sum {ι'} (s : Finset ι') (f : ι' → M) :
 #align direct_sum.decompose_sum DirectSum.decompose_sum
 
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 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_sum DirectSum.decompose_symm_sumₓ'. -/
 @[simp]
 theorem decompose_symm_sum {ι'} (s : Finset ι') (f : ι' → ⨁ i, ℳ i) :
@@ -266,10 +239,7 @@ theorem decompose_symm_sum {ι'} (s : Finset ι') (f : ι' → ⨁ i, ℳ i) :
 #align direct_sum.decompose_symm_sum DirectSum.decompose_symm_sum
 
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 Case conversion may be inaccurate. Consider using '#align direct_sum.sum_support_decompose DirectSum.sum_support_decomposeₓ'. -/
 theorem sum_support_decompose [∀ (i) (x : ℳ i), Decidable (x ≠ 0)] (r : M) :
     (∑ i in (decompose ℳ r).support, (decompose ℳ r i : M)) = r :=
@@ -305,10 +275,7 @@ variable [Decomposition ℳ]
 include M
 
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 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_neg DirectSum.decompose_negₓ'. -/
 @[simp]
 theorem decompose_neg (x : M) : decompose ℳ (-x) = -decompose ℳ x :=
@@ -316,10 +283,7 @@ theorem decompose_neg (x : M) : decompose ℳ (-x) = -decompose ℳ x :=
 #align direct_sum.decompose_neg DirectSum.decompose_neg
 
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 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_neg DirectSum.decompose_symm_negₓ'. -/
 @[simp]
 theorem decompose_symm_neg (x : ⨁ i, ℳ i) : (decompose ℳ).symm (-x) = -(decompose ℳ).symm x :=
@@ -327,10 +291,7 @@ theorem decompose_symm_neg (x : ⨁ i, ℳ i) : (decompose ℳ).symm (-x) = -(de
 #align direct_sum.decompose_symm_neg DirectSum.decompose_symm_neg
 
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 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_sub DirectSum.decompose_subₓ'. -/
 @[simp]
 theorem decompose_sub (x y : M) : decompose ℳ (x - y) = decompose ℳ x - decompose ℳ y :=
@@ -338,10 +299,7 @@ theorem decompose_sub (x y : M) : decompose ℳ (x - y) = decompose ℳ x - deco
 #align direct_sum.decompose_sub DirectSum.decompose_sub
 
 /- warning: direct_sum.decompose_symm_sub -> DirectSum.decompose_symm_sub is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_sub DirectSum.decompose_symm_subₓ'. -/
 @[simp]
 theorem decompose_symm_sub (x y : ⨁ i, ℳ i) :
@@ -376,10 +334,7 @@ def decomposeLinearEquiv : M ≃ₗ[R] ⨁ i, ℳ i :=
 #align direct_sum.decompose_linear_equiv DirectSum.decomposeLinearEquiv
 
 /- warning: direct_sum.decompose_smul -> DirectSum.decompose_smul is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (ℳ : ι -> (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4)) [_inst_5 : DirectSum.Decomposition.{u1, u3, u3} ι M (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_3 (Submodule.setLike.{u2, u3} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u2, u3} R M _inst_2 _inst_3 _inst_4) ℳ] (r : R) (x : M), Eq.{succ (max u1 u3)} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u2, u3} R M _inst_2 _inst_3 _inst_4)) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} M _inst_3 (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u2, u3} R 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(Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))) x) (AddCommMonoid.toAddMonoid.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))) x) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))))) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))) x) (Semiring.toMonoidWithZero.{u1} R _inst_2) (AddMonoid.toZero.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))) x) (AddCommMonoid.toAddMonoid.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))) x) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))))) (Module.toMulActionWithZero.{u1, max u3 u2} R ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))) x) _inst_2 (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))) (DirectSum.instModuleDirectSumInstAddCommMonoidDirectSum.{u1, u3, u2} R _inst_2 ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i)) (fun (i : ι) => Submodule.module.{u1, u2} R M _inst_2 _inst_3 _inst_4 (ℳ i)))))))) r (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i)))) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) 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_inst_4) (ℳ i)))) (DirectSum.decompose.{u3, u2, u2} ι M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_3 (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) ℳ _inst_5) x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_smul DirectSum.decompose_smulₓ'. -/
 @[simp]
 theorem decompose_smul (r : R) (x : M) : decompose ℳ (r • x) = r • decompose ℳ x :=

33c67ae6

bump to nightly-2023-05-21-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

7b1466d5

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Jujian Zhang
 
 ! This file was ported from Lean 3 source module algebra.direct_sum.decomposition
-! leanprover-community/mathlib commit 4e861f25ba5ceef42ba0712d8ffeb32f38ad6441
+! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Algebra.Module.Submodule.Basic
 /-!
 # Decompositions of additive monoids, groups, and modules into direct sums
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main definitions
 
 * `direct_sum.decomposition ℳ`: A typeclass to provide a constructive decomposition from

4e861f25

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -119,7 +119,7 @@ protected theorem Decomposition.inductionOn {p : M → Prop} (h_zero : p 0)
 lean 3 declaration is
   forall {ι : Type.{u1}} {M : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : SetLike.{u3, u2} σ M] [_inst_4 : AddSubmonoidClass.{u3, u2} σ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u1, u2, u3} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ], Eq.{max (succ u2) (succ (max u1 u2))} (M -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (DirectSum.Decomposition.decompose'.{u1, u2, u3} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 (fun (i : ι) => ℳ i) _inst_5) (coeFn.{max 1 (max (succ u2) (succ (max u1 u2))) (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (Equiv.{succ u2, succ (max u1 u2)} M (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} M (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) => M -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} M (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (DirectSum.decompose.{u1, u2, u3} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5))
 but is expected to have type
-  forall {ι : Type.{u3}} {M : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : SetLike.{u1, u2} σ M] [_inst_4 : AddSubmonoidClass.{u1, u2} σ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ], Eq.{max (succ u3) (succ u2)} (M -> (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (DirectSum.Decomposition.decompose'.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 (fun (i : ι) => ℳ i) _inst_5) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (DirectSum.decompose.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5))
+  forall {ι : Type.{u3}} {M : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : SetLike.{u1, u2} σ M] [_inst_4 : AddSubmonoidClass.{u1, u2} σ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ], Eq.{max (succ u3) (succ u2)} (M -> (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (DirectSum.Decomposition.decompose'.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 (fun (i : ι) => ℳ i) _inst_5) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (DirectSum.decompose.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5))
 Case conversion may be inaccurate. Consider using '#align direct_sum.decomposition.decompose'_eq DirectSum.Decomposition.decompose'_eqₓ'. -/
 @[simp]
 theorem Decomposition.decompose'_eq : Decomposition.decompose' = decompose ℳ :=
@@ -130,7 +130,7 @@ theorem Decomposition.decompose'_eq : Decomposition.decompose' = decompose ℳ :
 lean 3 declaration is
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 but is expected to have type
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=> Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (AddMonoid.toAddZeroClass.{u3} (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (AddCommMonoid.toAddMonoid.{u3} (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (AddMonoid.toAddZeroClass.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (AddCommMonoid.toAddMonoid.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x 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+  forall {ι : Type.{u1}} {M : Type.{u3}} {σ : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : SetLike.{u2, u3} σ M] [_inst_4 : AddSubmonoidClass.{u2, u3} σ M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u1, u3, u2} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ] {i : ι} (x : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))), Eq.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) => M) (FunLike.coe.{max (succ u1) (succ u3), succ u3, max (succ u1) (succ u3)} (AddMonoidHom.{u3, max u3 u1} (Subtype.{succ u3} M (fun 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 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_of DirectSum.decompose_symm_ofₓ'. -/
 @[simp]
 theorem decompose_symm_of {i : ι} (x : ℳ i) : (decompose ℳ).symm (DirectSum.of _ i x) = x :=
@@ -141,7 +141,7 @@ theorem decompose_symm_of {i : ι} (x : ℳ i) : (decompose ℳ).symm (DirectSum
 lean 3 declaration is
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 but is expected to have type
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+  forall {ι : Type.{u1}} {M : Type.{u3}} {σ : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : SetLike.{u2, u3} σ M] [_inst_4 : AddSubmonoidClass.{u2, u3} σ M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u1, u3, u2} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ] {i : ι} (x : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))), Eq.{max (succ u1) (succ u3)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x 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(AddCommMonoid.toAddMonoid.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (instAddCommMonoidDirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))))))) (DirectSum.of.{u1, u3} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)) i) x)
 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_coe DirectSum.decompose_coeₓ'. -/
 @[simp]
 theorem decompose_coe {i : ι} (x : ℳ i) : decompose ℳ (x : M) = DirectSum.of _ i x := by
@@ -152,7 +152,7 @@ theorem decompose_coe {i : ι} (x : ℳ i) : decompose ℳ (x : M) = DirectSum.o
 lean 3 declaration is
   forall {ι : Type.{u1}} {M : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : SetLike.{u3, u2} σ M] [_inst_4 : AddSubmonoidClass.{u3, u2} σ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u1, u2, u3} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ] {x : M} {i : ι} (hx : Membership.Mem.{u2, u3} M σ (SetLike.hasMem.{u3, u2} σ M _inst_3) x (ℳ i)), Eq.{succ (max u1 u2)} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (coeFn.{max 1 (max (succ u2) (succ (max u1 u2))) (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (Equiv.{succ u2, succ (max u1 u2)} M (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ 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=> Membership.Mem.{u2, u3} M σ (SetLike.hasMem.{u3, u2} σ M _inst_3) x (ℳ i)) x hx))
 but is expected to have type
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: M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))))))) (DirectSum.of.{u1, u3} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)) i) (Subtype.mk.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i)) x hx))
 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_of_mem DirectSum.decompose_of_memₓ'. -/
 theorem decompose_of_mem {x : M} {i : ι} (hx : x ∈ ℳ i) :
     decompose ℳ x = DirectSum.of (fun i => ℳ i) i ⟨x, hx⟩ :=
@@ -163,7 +163,7 @@ theorem decompose_of_mem {x : M} {i : ι} (hx : x ∈ ℳ i) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {M : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : SetLike.{u3, u2} σ M] [_inst_4 : AddSubmonoidClass.{u3, u2} σ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u1, u2, u3} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ] {x : M} {i : ι}, (Membership.Mem.{u2, u3} M σ (SetLike.hasMem.{u3, u2} σ M _inst_3) x (ℳ i)) -> (Eq.{succ u2} M ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) M (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u3} M σ (SetLike.hasMem.{u3, u2} σ M _inst_3) x (ℳ i)))))) (coeFn.{succ (max u1 u2), max (succ u1) (succ u2)} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (coeFn.{max 1 (max (succ u2) (succ (max u1 u2))) (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (Equiv.{succ u2, succ (max u1 u2)} M (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} M (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) => M -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} M (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (DirectSum.decompose.{u1, u2, u3} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5) x) i)) x)
 but is expected to have type
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+  forall {ι : Type.{u1}} {M : Type.{u3}} {σ : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : SetLike.{u2, u3} σ M] [_inst_4 : AddSubmonoidClass.{u2, u3} σ M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u1, u3, u2} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ] {x : M} {i : ι}, (Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i)) -> (Eq.{succ u3} M (Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x (SetLike.coe.{u2, u3} σ M _inst_3 (ℳ i))) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) i) i) _x) (Dfinsupp.funLike.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)) i))) i)) (FunLike.coe.{max (succ u1) (succ u3), succ u3, max (succ u1) (succ u3)} (Equiv.{succ u3, max (succ u3) (succ u1)} M (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} M (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (DirectSum.decompose.{u1, u3, u2} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5) x) i)) x)
 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_of_mem_same DirectSum.decompose_of_mem_sameₓ'. -/
 theorem decompose_of_mem_same {x : M} {i : ι} (hx : x ∈ ℳ i) : (decompose ℳ x i : M) = x := by
   rw [decompose_of_mem _ hx, DirectSum.of_eq_same, Subtype.coe_mk]
@@ -173,7 +173,7 @@ theorem decompose_of_mem_same {x : M} {i : ι} (hx : x ∈ ℳ i) : (decompose 
 lean 3 declaration is
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 but is expected to have type
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+  forall {ι : Type.{u1}} {M : Type.{u3}} {σ : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : SetLike.{u2, u3} σ M] [_inst_4 : AddSubmonoidClass.{u2, u3} σ M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u1, u3, u2} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ] {x : M} {i : ι} {j : ι}, (Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i)) -> (Ne.{succ u1} ι i j) -> (Eq.{succ u3} M (Subtype.val.{succ u3} M (fun (x : M) => Membership.mem.{u3, u3} M (Set.{u3} M) (Set.instMembershipSet.{u3} M) x (SetLike.coe.{u2, u3} σ M _inst_3 (ℳ j))) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (Dfinsupp.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) i) i) _x) (Dfinsupp.funLike.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)) i))) i)) (FunLike.coe.{max (succ u1) (succ u3), succ u3, max (succ u1) (succ u3)} (Equiv.{succ u3, max (succ u3) (succ u1)} M (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} M (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (DirectSum.decompose.{u1, u3, u2} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5) x) j)) (OfNat.ofNat.{u3} M 0 (Zero.toOfNat0.{u3} M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_of_mem_ne DirectSum.decompose_of_mem_neₓ'. -/
 theorem decompose_of_mem_ne {x : M} {i j : ι} (hx : x ∈ ℳ i) (hij : i ≠ j) :
     (decompose ℳ x j : M) = 0 := by
@@ -197,7 +197,7 @@ def decomposeAddEquiv : M ≃+ ⨁ i, ℳ i :=
 lean 3 declaration is
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 but is expected to have type
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+  forall {ι : Type.{u3}} {M : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : SetLike.{u1, u2} σ M] [_inst_4 : AddSubmonoidClass.{u1, u2} σ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ], Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (DirectSum.decompose.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5) (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) (OfNat.ofNat.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) 0 (Zero.toOfNat0.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) (AddMonoid.toZero.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) (AddCommMonoid.toAddMonoid.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))))))
 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_zero DirectSum.decompose_zeroₓ'. -/
 @[simp]
 theorem decompose_zero : decompose ℳ (0 : M) = 0 :=
@@ -208,7 +208,7 @@ theorem decompose_zero : decompose ℳ (0 : M) = 0 :=
 lean 3 declaration is
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 but is expected to have type
-  forall {ι : Type.{u2}} {M : Type.{u3}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} ι] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : SetLike.{u1, u3} σ M] [_inst_4 : AddSubmonoidClass.{u1, u3} σ M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u2, u3, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ], Eq.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) => M) (OfNat.ofNat.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) 0 (Zero.toOfNat0.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (AddMonoid.toZero.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (AddCommMonoid.toAddMonoid.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (instAddCommMonoidDirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))))))) (FunLike.coe.{max (succ u2) (succ u3), max (succ u2) (succ u3), succ u3} (Equiv.{max (succ u2) (succ u3), succ u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) M) (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (fun (_x : DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) => M) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u3), succ u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) M) (Equiv.symm.{succ u3, max (succ u2) (succ u3)} M (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (DirectSum.decompose.{u2, u3, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5)) (OfNat.ofNat.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) 0 (Zero.toOfNat0.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (AddMonoid.toZero.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (AddCommMonoid.toAddMonoid.{max u2 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+  forall {ι : Type.{u2}} {M : Type.{u3}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} ι] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : SetLike.{u1, u3} σ M] [_inst_4 : AddSubmonoidClass.{u1, u3} σ M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u2, u3, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ], Eq.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) => M) (OfNat.ofNat.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 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(SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))))))) (FunLike.coe.{max (succ u2) (succ u3), max (succ u2) (succ u3), succ u3} (Equiv.{max (succ u2) (succ u3), succ u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) M) (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (fun (_x : DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) => M) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u3), succ u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) M) (Equiv.symm.{succ u3, max (succ u2) (succ u3)} M (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (DirectSum.decompose.{u2, u3, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5)) (OfNat.ofNat.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) 0 (Zero.toOfNat0.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (AddMonoid.toZero.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (AddCommMonoid.toAddMonoid.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (instAddCommMonoidDirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u1} M σ (SetLike.instMembership.{u1, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))))))) (OfNat.ofNat.{u3} M 0 (Zero.toOfNat0.{u3} M (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2))))
 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_zero DirectSum.decompose_symm_zeroₓ'. -/
 @[simp]
 theorem decompose_symm_zero : (decompose ℳ).symm 0 = (0 : M) :=
@@ -219,7 +219,7 @@ theorem decompose_symm_zero : (decompose ℳ).symm 0 = (0 : M) :=
 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 direct_sum.decompose_add DirectSum.decompose_addₓ'. -/
 @[simp]
 theorem decompose_add (x y : M) : decompose ℳ (x + y) = decompose ℳ x + decompose ℳ y :=
@@ -230,7 +230,7 @@ theorem decompose_add (x y : M) : decompose ℳ (x + y) = decompose ℳ x + deco
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_add DirectSum.decompose_symm_addₓ'. -/
 @[simp]
 theorem decompose_symm_add (x y : ⨁ i, ℳ i) :
@@ -242,7 +242,7 @@ theorem decompose_symm_add (x y : ⨁ i, ℳ i) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {M : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : SetLike.{u3, u2} σ M] [_inst_4 : AddSubmonoidClass.{u3, u2} σ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u1, u2, u3} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ] {ι' : Type.{u4}} (s : Finset.{u4} ι') (f : ι' -> M), Eq.{succ (max u1 u2)} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (coeFn.{max 1 (max (succ u2) (succ (max u1 u2))) (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (Equiv.{succ u2, succ (max u1 u2)} M (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} M (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) => M -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} M (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (DirectSum.decompose.{u1, u2, u3} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5) (Finset.sum.{u2, u4} M ι' _inst_2 s (fun (i : ι') => f i))) (Finset.sum.{max u1 u2, u4} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) ι' (DirectSum.addCommMonoid.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) s (fun (i : ι') => coeFn.{max 1 (max (succ u2) (succ (max u1 u2))) (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (Equiv.{succ u2, succ (max u1 u2)} M (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} M (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) => M -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} M (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (DirectSum.decompose.{u1, u2, u3} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5) (f i)))
 but is expected to have type
-  forall {ι : Type.{u3}} {M : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : SetLike.{u1, u2} σ M] [_inst_4 : AddSubmonoidClass.{u1, u2} σ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ] {ι' : Type.{u4}} (s : Finset.{u4} ι') (f : ι' -> M), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (Finset.sum.{u2, u4} M ι' _inst_2 s (fun (i : ι') => f i))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (DirectSum.decompose.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5) (Finset.sum.{u2, u4} M ι' _inst_2 s (fun (i : ι') => f i))) (Finset.sum.{max u3 u2, u4} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) ι' (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) s (fun (i : ι') => FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (DirectSum.decompose.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5) (f i)))
+  forall {ι : Type.{u3}} {M : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : SetLike.{u1, u2} σ M] [_inst_4 : AddSubmonoidClass.{u1, u2} σ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ] {ι' : Type.{u4}} (s : Finset.{u4} ι') (f : ι' -> M), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (Finset.sum.{u2, u4} M ι' _inst_2 s (fun (i : ι') => f i))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (DirectSum.decompose.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5) (Finset.sum.{u2, u4} M ι' _inst_2 s (fun (i : ι') => f i))) (Finset.sum.{max u3 u2, u4} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) ι' (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) s (fun (i : ι') => FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (DirectSum.decompose.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5) (f i)))
 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_sum DirectSum.decompose_sumₓ'. -/
 @[simp]
 theorem decompose_sum {ι'} (s : Finset ι') (f : ι' → M) :
@@ -254,7 +254,7 @@ theorem decompose_sum {ι'} (s : Finset ι') (f : ι' → M) :
 lean 3 declaration is
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 but is expected to have type
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M _inst_2 σ _inst_3 _inst_4 (ℳ i))) => M) (Finset.sum.{max u3 u2, u4} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) ι' (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) s (fun (i : ι') => f i))) (FunLike.coe.{max (succ u3) (succ u2), max (succ u3) (succ u2), succ u2} (Equiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) M) 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: ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) => M) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) M) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (DirectSum.decompose.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5)) (f i)))
+  forall {ι : Type.{u3}} {M : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : SetLike.{u1, u2} σ M] [_inst_4 : AddSubmonoidClass.{u1, u2} σ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ] {ι' : Type.{u4}} (s : Finset.{u4} ι') (f : ι' -> (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} 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: ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) => M) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) M) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) (DirectSum.decompose.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5)) (f i)))
 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_sum DirectSum.decompose_symm_sumₓ'. -/
 @[simp]
 theorem decompose_symm_sum {ι'} (s : Finset ι') (f : ι' → ⨁ i, ℳ i) :
@@ -266,7 +266,7 @@ theorem decompose_symm_sum {ι'} (s : Finset ι') (f : ι' → ⨁ i, ℳ i) :
 lean 3 declaration is
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 but is expected to have type
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Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (DirectSum.decompose.{u1, u3, u2} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5) r) i))) r
+  forall {ι : Type.{u1}} {M : Type.{u3}} {σ : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : SetLike.{u2, u3} σ M] [_inst_4 : AddSubmonoidClass.{u2, u3} σ M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u1, u3, u2} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ] [_inst_6 : forall (i : ι) (x : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))), Decidable (Ne.{succ u3} (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) x (OfNat.ofNat.{u3} (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) 0 (Zero.toOfNat0.{u3} (Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (ZeroMemClass.zero.{u2, u3} σ M _inst_3 (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (AddSubmonoidClass.toZeroMemClass.{u2, u3} σ M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) _inst_3 _inst_4) (ℳ i)))))] (r : M), Eq.{succ u3} M (Finset.sum.{u3, u1} M ι _inst_2 (Dfinsupp.support.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) i) (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)) i))) (fun (i : ι) (x : Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) => _inst_6 i x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, max (succ u1) (succ u3)} (Equiv.{succ u3, max (succ u3) (succ u1)} M (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} M (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} M 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(SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)) i))) i)) (FunLike.coe.{max (succ u1) (succ u3), succ u3, max (succ u1) (succ u3)} (Equiv.{succ u3, max (succ u3) (succ u1)} M (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} M (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} M (fun (x : M) => Membership.mem.{u3, u2} M σ (SetLike.instMembership.{u2, u3} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} M _inst_2 σ _inst_3 _inst_4 (ℳ i)))) (DirectSum.decompose.{u1, u3, u2} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ _inst_5) r) i))) r
 Case conversion may be inaccurate. Consider using '#align direct_sum.sum_support_decompose DirectSum.sum_support_decomposeₓ'. -/
 theorem sum_support_decompose [∀ (i) (x : ℳ i), Decidable (x ≠ 0)] (r : M) :
     (∑ i in (decompose ℳ r).support, (decompose ℳ r i : M)) = r :=
@@ -305,7 +305,7 @@ include M
 lean 3 declaration is
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 but is expected to have type
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+  forall {ι : Type.{u3}} {M : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : SetLike.{u1, u2} σ M] [_inst_4 : AddSubgroupClass.{u1, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddSubgroupClass.toAddSubmonoidClass.{u1, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3 _inst_4) ℳ] (x : M), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) σ _inst_3 (AddSubgroupClass.toAddSubmonoidClass.{u1, u2} σ 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_inst_4) (ℳ i))) x) (AddCommGroup.toDivisionAddCommMonoid.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) σ _inst_3 (AddSubgroupClass.toAddSubmonoidClass.{u1, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3 _inst_4) (ℳ i))) x) (DirectSum.addCommGroupSetLike.{u3, u2, u1} ι M σ _inst_2 _inst_3 _inst_4 (fun (i : ι) => ℳ i))))))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) σ _inst_3 (AddSubgroupClass.toAddSubmonoidClass.{u1, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3 _inst_4) (ℳ i)))) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) σ _inst_3 (AddSubgroupClass.toAddSubmonoidClass.{u1, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3 _inst_4) (ℳ i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) σ _inst_3 (AddSubgroupClass.toAddSubmonoidClass.{u1, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3 _inst_4) (ℳ i)))) (DirectSum.decompose.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddSubgroupClass.toAddSubmonoidClass.{u1, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3 _inst_4) ℳ _inst_5) x))
 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_neg DirectSum.decompose_negₓ'. -/
 @[simp]
 theorem decompose_neg (x : M) : decompose ℳ (-x) = -decompose ℳ x :=
@@ -316,7 +316,7 @@ theorem decompose_neg (x : M) : decompose ℳ (-x) = -decompose ℳ x :=
 lean 3 declaration is
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_inst_2)) _inst_3 _inst_4) (ℳ i))) (SubNegMonoid.toHasNeg.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) σ _inst_3 (AddSubgroupClass.to_addSubmonoidClass.{u3, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3 _inst_4) (ℳ i))) (AddGroup.toSubNegMonoid.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) σ _inst_3 (AddSubgroupClass.to_addSubmonoidClass.{u3, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3 _inst_4) (ℳ i))) (AddCommGroup.toAddGroup.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => 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(AddSubgroupClass.to_addSubmonoidClass.{u3, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3 _inst_4) (ℳ i))) M) (fun (_x : Equiv.{succ (max u1 u2), succ u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) σ _inst_3 (AddSubgroupClass.to_addSubmonoidClass.{u3, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3 _inst_4) (ℳ i))) M) => (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) σ _inst_3 (AddSubgroupClass.to_addSubmonoidClass.{u3, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3 _inst_4) (ℳ i))) -> M) (Equiv.hasCoeToFun.{succ (max u1 u2), succ u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) σ _inst_3 (AddSubgroupClass.to_addSubmonoidClass.{u3, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3 _inst_4) (ℳ i))) M) (Equiv.symm.{succ u2, succ (max u1 u2)} M (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ M _inst_3) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) σ _inst_3 (AddSubgroupClass.to_addSubmonoidClass.{u3, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3 _inst_4) (ℳ i))) (DirectSum.decompose.{u1, u2, u3} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddSubgroupClass.to_addSubmonoidClass.{u3, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3 _inst_4) ℳ _inst_5)) x))
 but is expected to have type
-  forall {ι : Type.{u3}} {M : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : SetLike.{u1, u2} σ M] [_inst_4 : AddSubgroupClass.{u1, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddSubgroupClass.toAddSubmonoidClass.{u1, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3 _inst_4) ℳ] (x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u1} M σ (SetLike.instMembership.{u1, u2} σ M _inst_3) x (ℳ i))) i) (AddSubgroupClass.toAddCommGroup.{u1, u2} σ (ℳ i) M _inst_2 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 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_neg DirectSum.decompose_symm_negₓ'. -/
 @[simp]
 theorem decompose_symm_neg (x : ⨁ i, ℳ i) : (decompose ℳ).symm (-x) = -(decompose ℳ).symm x :=
@@ -327,7 +327,7 @@ theorem decompose_symm_neg (x : ⨁ i, ℳ i) : (decompose ℳ).symm (-x) = -(de
 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 direct_sum.decompose_sub DirectSum.decompose_subₓ'. -/
 @[simp]
 theorem decompose_sub (x y : M) : decompose ℳ (x - y) = decompose ℳ x - decompose ℳ y :=
@@ -338,7 +338,7 @@ theorem decompose_sub (x y : M) : decompose ℳ (x - y) = decompose ℳ x - deco
 lean 3 declaration is
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 but is expected to have type
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u2} σ M _inst_3) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) σ _inst_3 (AddSubgroupClass.toAddSubmonoidClass.{u1, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3 _inst_4) (ℳ i))) (DirectSum.decompose.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (AddSubgroupClass.toAddSubmonoidClass.{u1, u2} σ M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_2)) _inst_3 _inst_4) ℳ _inst_5)) y))
 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_sub DirectSum.decompose_symm_subₓ'. -/
 @[simp]
 theorem decompose_symm_sub (x y : ⨁ i, ℳ i) :
@@ -376,7 +376,7 @@ def decomposeLinearEquiv : M ≃ₗ[R] ⨁ i, ℳ i :=
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : Semiring.{u2} R] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : Module.{u2, u3} R M _inst_2 _inst_3] (ℳ : ι -> (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4)) [_inst_5 : DirectSum.Decomposition.{u1, u3, u3} ι M (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_3 (Submodule.setLike.{u2, u3} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u2, u3} R M _inst_2 _inst_3 _inst_4) ℳ] (r : R) (x : M), Eq.{succ (max u1 u3)} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u2, u3} R M _inst_2 _inst_3 _inst_4)) (ℳ i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} M _inst_3 (Submodule.{u2, u3} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u2, u3} R 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 but is expected to have type
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_inst_4) (ℳ i))) x) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))))) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun 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(Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))))) (Module.toMulActionWithZero.{u1, max u3 u2} R ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))) x) _inst_2 (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 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_inst_3 _inst_4) (ℳ i)) (fun (i : ι) => Submodule.module.{u1, u2} R M _inst_2 _inst_3 _inst_4 (ℳ i)))))))) r (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i)))) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i)))) (DirectSum.decompose.{u3, u2, u2} ι M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_3 (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) ℳ _inst_5) x))
 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_smul DirectSum.decompose_smulₓ'. -/
 @[simp]
 theorem decompose_smul (r : R) (x : M) : decompose ℳ (r • x) = r • decompose ℳ x :=

4e861f25

bump to nightly-2023-05-18-14

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

32388111

Diff

@@ -46,6 +46,7 @@ variable [DecidableEq ι] [AddCommMonoid M]
 
 variable [SetLike σ M] [AddSubmonoidClass σ M] (ℳ : ι → σ)
 
+#print DirectSum.Decomposition /-
 /-- A decomposition is an equivalence between an additive monoid `M` and a direct sum of additive
 submonoids `ℳ i` of that `M`, such that the "recomposition" is canonical. This definition also
 works for additive groups and modules.
@@ -57,6 +58,7 @@ class Decomposition where
   left_inv : Function.LeftInverse (DirectSum.coeAddMonoidHom ℳ) decompose'
   right_inv : Function.RightInverse (DirectSum.coeAddMonoidHom ℳ) decompose'
 #align direct_sum.decomposition DirectSum.Decomposition
+-/
 
 include M
 
@@ -70,10 +72,17 @@ instance : Subsingleton (Decomposition ℳ) :=
 
 variable [Decomposition ℳ]
 
+/- warning: direct_sum.decomposition.is_internal -> DirectSum.Decomposition.isInternal is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {M : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : SetLike.{u3, u2} σ M] [_inst_4 : AddSubmonoidClass.{u3, u2} σ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u1, u2, u3} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ], DirectSum.IsInternal.{u1, u2, u3} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ
+but is expected to have type
+  forall {ι : Type.{u3}} {M : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : SetLike.{u1, u2} σ M] [_inst_4 : AddSubmonoidClass.{u1, u2} σ M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) _inst_3] (ℳ : ι -> σ) [_inst_5 : DirectSum.Decomposition.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ], DirectSum.IsInternal.{u3, u2, u1} ι M σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 ℳ
+Case conversion may be inaccurate. Consider using '#align direct_sum.decomposition.is_internal DirectSum.Decomposition.isInternalₓ'. -/
 protected theorem Decomposition.isInternal : DirectSum.IsInternal ℳ :=
   ⟨Decomposition.right_inv.Injective, Decomposition.left_inv.Surjective⟩
 #align direct_sum.decomposition.is_internal DirectSum.Decomposition.isInternal
 
+#print DirectSum.decompose /-
 /-- If `M` is graded by `ι` with degree `i` component `ℳ i`, then it is isomorphic as
 to a direct sum of components. This is the canonical spelling of the `decompose'` field. -/
 def decompose : M ≃ ⨁ i, ℳ i where
@@ -82,7 +91,14 @@ def decompose : M ≃ ⨁ i, ℳ i where
   left_inv := Decomposition.left_inv
   right_inv := Decomposition.right_inv
 #align direct_sum.decompose DirectSum.decompose
+-/
 
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+Case conversion may be inaccurate. Consider using '#align direct_sum.decomposition.induction_on DirectSum.Decomposition.inductionOnₓ'. -/
 protected theorem Decomposition.inductionOn {p : M → Prop} (h_zero : p 0)
     (h_homogeneous : ∀ {i} (m : ℳ i), p (m : M)) (h_add : ∀ m m' : M, p m → p m' → p (m + m')) :
     ∀ m, p m :=
@@ -99,35 +115,77 @@ protected theorem Decomposition.inductionOn {p : M → Prop} (h_zero : p 0)
     AddSubmonoid.iSup_induction ℳ' (mem m) (fun i m h => h_homogeneous ⟨m, h⟩) h_zero h_add
 #align direct_sum.decomposition.induction_on DirectSum.Decomposition.inductionOn
 
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 @[simp]
 theorem Decomposition.decompose'_eq : Decomposition.decompose' = decompose ℳ :=
   rfl
 #align direct_sum.decomposition.decompose'_eq DirectSum.Decomposition.decompose'_eq
 
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+Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_of DirectSum.decompose_symm_ofₓ'. -/
 @[simp]
 theorem decompose_symm_of {i : ι} (x : ℳ i) : (decompose ℳ).symm (DirectSum.of _ i x) = x :=
   DirectSum.coeAddMonoidHom_of ℳ _ _
 #align direct_sum.decompose_symm_of DirectSum.decompose_symm_of
 
+/- warning: direct_sum.decompose_coe -> DirectSum.decompose_coe 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 direct_sum.decompose_coe DirectSum.decompose_coeₓ'. -/
 @[simp]
 theorem decompose_coe {i : ι} (x : ℳ i) : decompose ℳ (x : M) = DirectSum.of _ i x := by
   rw [← decompose_symm_of, Equiv.apply_symm_apply]
 #align direct_sum.decompose_coe DirectSum.decompose_coe
 
+/- warning: direct_sum.decompose_of_mem -> DirectSum.decompose_of_mem is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_of_mem DirectSum.decompose_of_memₓ'. -/
 theorem decompose_of_mem {x : M} {i : ι} (hx : x ∈ ℳ i) :
     decompose ℳ x = DirectSum.of (fun i => ℳ i) i ⟨x, hx⟩ :=
   decompose_coe _ ⟨x, hx⟩
 #align direct_sum.decompose_of_mem DirectSum.decompose_of_mem
 
+/- warning: direct_sum.decompose_of_mem_same -> DirectSum.decompose_of_mem_same is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_of_mem_same DirectSum.decompose_of_mem_sameₓ'. -/
 theorem decompose_of_mem_same {x : M} {i : ι} (hx : x ∈ ℳ i) : (decompose ℳ x i : M) = x := by
   rw [decompose_of_mem _ hx, DirectSum.of_eq_same, Subtype.coe_mk]
 #align direct_sum.decompose_of_mem_same DirectSum.decompose_of_mem_same
 
+/- warning: direct_sum.decompose_of_mem_ne -> DirectSum.decompose_of_mem_ne is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_of_mem_ne DirectSum.decompose_of_mem_neₓ'. -/
 theorem decompose_of_mem_ne {x : M} {i j : ι} (hx : x ∈ ℳ i) (hij : i ≠ j) :
     (decompose ℳ x j : M) = 0 := by
   rw [decompose_of_mem _ hx, DirectSum.of_eq_of_ne _ _ _ _ hij, ZeroMemClass.coe_zero]
 #align direct_sum.decompose_of_mem_ne DirectSum.decompose_of_mem_ne
 
+/- warning: direct_sum.decompose_add_equiv -> DirectSum.decomposeAddEquiv is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_add_equiv DirectSum.decomposeAddEquivₓ'. -/
 /-- If `M` is graded by `ι` with degree `i` component `ℳ i`, then it is isomorphic as
 an additive monoid to a direct sum of components. -/
 @[simps (config := { fullyApplied := false })]
@@ -135,39 +193,81 @@ def decomposeAddEquiv : M ≃+ ⨁ i, ℳ i :=
   AddEquiv.symm { (decompose ℳ).symm with map_add' := map_add (DirectSum.coeAddMonoidHom ℳ) }
 #align direct_sum.decompose_add_equiv DirectSum.decomposeAddEquiv
 
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+Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_zero DirectSum.decompose_zeroₓ'. -/
 @[simp]
 theorem decompose_zero : decompose ℳ (0 : M) = 0 :=
   map_zero (decomposeAddEquiv ℳ)
 #align direct_sum.decompose_zero DirectSum.decompose_zero
 
+/- warning: direct_sum.decompose_symm_zero -> DirectSum.decompose_symm_zero is a dubious translation:
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 @[simp]
 theorem decompose_symm_zero : (decompose ℳ).symm 0 = (0 : M) :=
   map_zero (decomposeAddEquiv ℳ).symm
 #align direct_sum.decompose_symm_zero DirectSum.decompose_symm_zero
 
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 @[simp]
 theorem decompose_add (x y : M) : decompose ℳ (x + y) = decompose ℳ x + decompose ℳ y :=
   map_add (decomposeAddEquiv ℳ) x y
 #align direct_sum.decompose_add DirectSum.decompose_add
 
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 @[simp]
 theorem decompose_symm_add (x y : ⨁ i, ℳ i) :
     (decompose ℳ).symm (x + y) = (decompose ℳ).symm x + (decompose ℳ).symm y :=
   map_add (decomposeAddEquiv ℳ).symm x y
 #align direct_sum.decompose_symm_add DirectSum.decompose_symm_add
 
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 @[simp]
 theorem decompose_sum {ι'} (s : Finset ι') (f : ι' → M) :
     decompose ℳ (∑ i in s, f i) = ∑ i in s, decompose ℳ (f i) :=
   map_sum (decomposeAddEquiv ℳ) f s
 #align direct_sum.decompose_sum DirectSum.decompose_sum
 
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+Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_sum DirectSum.decompose_symm_sumₓ'. -/
 @[simp]
 theorem decompose_symm_sum {ι'} (s : Finset ι') (f : ι' → ⨁ i, ℳ i) :
     (decompose ℳ).symm (∑ i in s, f i) = ∑ i in s, (decompose ℳ).symm (f i) :=
   map_sum (decomposeAddEquiv ℳ).symm f s
 #align direct_sum.decompose_symm_sum DirectSum.decompose_symm_sum
 
+/- warning: direct_sum.sum_support_decompose -> DirectSum.sum_support_decompose is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align direct_sum.sum_support_decompose DirectSum.sum_support_decomposeₓ'. -/
 theorem sum_support_decompose [∀ (i) (x : ℳ i), Decidable (x ≠ 0)] (r : M) :
     (∑ i in (decompose ℳ r).support, (decompose ℳ r i : M)) = r :=
   by
@@ -179,6 +279,7 @@ theorem sum_support_decompose [∀ (i) (x : ℳ i), Decidable (x ≠ 0)] (r : M)
 
 end AddCommMonoid
 
+#print DirectSum.addCommGroupSetLike /-
 /-- The `-` in the statements below doesn't resolve without this line.
 
 This seems to a be a problem of synthesized vs inferred typeclasses disagreeing. If we replace
@@ -188,6 +289,7 @@ be found by unification rather than synthesis, then everything works fine withou
 instance addCommGroupSetLike [AddCommGroup M] [SetLike σ M] [AddSubgroupClass σ M] (ℳ : ι → σ) :
     AddCommGroup (⨁ i, ℳ i) := by infer_instance
 #align direct_sum.add_comm_group_set_like DirectSum.addCommGroupSetLike
+-/
 
 section AddCommGroup
 
@@ -199,21 +301,45 @@ variable [Decomposition ℳ]
 
 include M
 
+/- warning: direct_sum.decompose_neg -> DirectSum.decompose_neg is a dubious translation:
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 @[simp]
 theorem decompose_neg (x : M) : decompose ℳ (-x) = -decompose ℳ x :=
   map_neg (decomposeAddEquiv ℳ) x
 #align direct_sum.decompose_neg DirectSum.decompose_neg
 
+/- warning: direct_sum.decompose_symm_neg -> DirectSum.decompose_symm_neg is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_neg DirectSum.decompose_symm_negₓ'. -/
 @[simp]
 theorem decompose_symm_neg (x : ⨁ i, ℳ i) : (decompose ℳ).symm (-x) = -(decompose ℳ).symm x :=
   map_neg (decomposeAddEquiv ℳ).symm x
 #align direct_sum.decompose_symm_neg DirectSum.decompose_symm_neg
 
+/- warning: direct_sum.decompose_sub -> DirectSum.decompose_sub is a dubious translation:
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 @[simp]
 theorem decompose_sub (x y : M) : decompose ℳ (x - y) = decompose ℳ x - decompose ℳ y :=
   map_sub (decomposeAddEquiv ℳ) x y
 #align direct_sum.decompose_sub DirectSum.decompose_sub
 
+/- warning: direct_sum.decompose_symm_sub -> DirectSum.decompose_symm_sub is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_sub DirectSum.decompose_symm_subₓ'. -/
 @[simp]
 theorem decompose_symm_sub (x y : ⨁ i, ℳ i) :
     (decompose ℳ).symm (x - y) = (decompose ℳ).symm x - (decompose ℳ).symm y :=
@@ -232,6 +358,12 @@ variable [Decomposition ℳ]
 
 include M
 
+/- warning: direct_sum.decompose_linear_equiv -> DirectSum.decomposeLinearEquiv is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_linear_equiv DirectSum.decomposeLinearEquivₓ'. -/
 /-- If `M` is graded by `ι` with degree `i` component `ℳ i`, then it is isomorphic as
 a module to a direct sum of components. -/
 @[simps (config := { fullyApplied := false })]
@@ -240,6 +372,12 @@ def decomposeLinearEquiv : M ≃ₗ[R] ⨁ i, ℳ i :=
     { (decomposeAddEquiv ℳ).symm with map_smul' := map_smul (DirectSum.coeLinearMap ℳ) }
 #align direct_sum.decompose_linear_equiv DirectSum.decomposeLinearEquiv
 
+/- warning: direct_sum.decompose_smul -> DirectSum.decompose_smul is a dubious translation:
+lean 3 declaration is
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(SMulWithZero.toSMulZeroClass.{u1, max u3 u2} R ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))) x) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_2)) (AddMonoid.toZero.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))) x) (AddCommMonoid.toAddMonoid.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))) x) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))))) (MulActionWithZero.toSMulWithZero.{u1, max u3 u2} R ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))) x) (Semiring.toMonoidWithZero.{u1} R _inst_2) (AddMonoid.toZero.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))) x) (AddCommMonoid.toAddMonoid.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))) x) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))))) (Module.toMulActionWithZero.{u1, max u3 u2} R ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))) x) _inst_2 (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))) (DirectSum.instModuleDirectSumInstAddCommMonoidDirectSum.{u1, u3, u2} R _inst_2 ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i)) (fun (i : ι) => Submodule.module.{u1, u2} R M _inst_2 _inst_3 _inst_4 (ℳ i)))))))) r (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i)))) M (fun (_x : M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : M) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} M (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} M (fun (x : M) => Membership.mem.{u2, u2} M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4)) x (ℳ i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} M _inst_3 (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) (ℳ i)))) (DirectSum.decompose.{u3, u2, u2} ι M (Submodule.{u1, u2} R M _inst_2 _inst_3 _inst_4) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_3 (Submodule.setLike.{u1, u2} R M _inst_2 _inst_3 _inst_4) (Submodule.addSubmonoidClass.{u1, u2} R M _inst_2 _inst_3 _inst_4) ℳ _inst_5) x))
+Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_smul DirectSum.decompose_smulₓ'. -/
 @[simp]
 theorem decompose_smul (r : R) (x : M) : decompose ℳ (r • x) = r • decompose ℳ x :=
   map_smul (decomposeLinearEquiv ℳ) r x

4e861f25

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -93,10 +93,10 @@ protected theorem Decomposition.inductionOn {p : M → Prop} (h_zero : p 0)
     { decompose' := DirectSum.decompose ℳ
       left_inv := fun _ => (decompose ℳ).left_inv _
       right_inv := fun _ => (decompose ℳ).right_inv _ }
-  have mem : ∀ m, m ∈ supᵢ ℳ' := fun m =>
-    (DirectSum.IsInternal.addSubmonoid_supᵢ_eq_top ℳ' (decomposition.is_internal ℳ')).symm ▸ trivial
+  have mem : ∀ m, m ∈ iSup ℳ' := fun m =>
+    (DirectSum.IsInternal.addSubmonoid_iSup_eq_top ℳ' (decomposition.is_internal ℳ')).symm ▸ trivial
   exact fun m =>
-    AddSubmonoid.supᵢ_induction ℳ' (mem m) (fun i m h => h_homogeneous ⟨m, h⟩) h_zero h_add
+    AddSubmonoid.iSup_induction ℳ' (mem m) (fun i m h => h_homogeneous ⟨m, h⟩) h_zero h_add
 #align direct_sum.decomposition.induction_on DirectSum.Decomposition.inductionOn
 
 @[simp]

4e861f25

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

4e861f25

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

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

75c86f04

Diff

@@ -40,7 +40,6 @@ namespace DirectSum
 section AddCommMonoid
 
 variable [DecidableEq ι] [AddCommMonoid M]
-
 variable [SetLike σ M] [AddSubmonoidClass σ M] (ℳ : ι → σ)
 
 /-- A decomposition is an equivalence between an additive monoid `M` and a direct sum of additive
@@ -219,9 +218,7 @@ instance addCommGroupSetLike [AddCommGroup M] [SetLike σ M] [AddSubgroupClass 
 section AddCommGroup
 
 variable [DecidableEq ι] [AddCommGroup M]
-
 variable [SetLike σ M] [AddSubgroupClass σ M] (ℳ : ι → σ)
-
 variable [Decomposition ℳ]
 
 @[simp]
@@ -250,7 +247,6 @@ end AddCommGroup
 section Module
 
 variable [DecidableEq ι] [Semiring R] [AddCommMonoid M] [Module R M]
-
 variable (ℳ : ι → Submodule R M)
 
 /-- A convenience method to construct a decomposition from an `LinearMap`, such that the proofs

4e861f25

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

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

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

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

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

82656743

Diff

@@ -72,8 +72,8 @@ abbrev Decomposition.ofAddHom (decompose : M →+ ⨁ i, ℳ i)
     (h_left_inv : (DirectSum.coeAddMonoidHom ℳ).comp decompose = .id _)
     (h_right_inv : decompose.comp (DirectSum.coeAddMonoidHom ℳ) = .id _) : Decomposition ℳ where
   decompose' := decompose
-  left_inv := FunLike.congr_fun h_left_inv
-  right_inv := FunLike.congr_fun h_right_inv
+  left_inv := DFunLike.congr_fun h_left_inv
+  right_inv := DFunLike.congr_fun h_right_inv
 
 /-- Noncomputably conjure a decomposition instance from a `DirectSum.IsInternal` proof. -/
 noncomputable def IsInternal.chooseDecomposition (h : IsInternal ℳ) :
@@ -259,8 +259,8 @@ abbrev Decomposition.ofLinearMap (decompose : M →ₗ[R] ⨁ i, ℳ i)
     (h_left_inv : DirectSum.coeLinearMap ℳ ∘ₗ decompose = .id)
     (h_right_inv : decompose ∘ₗ DirectSum.coeLinearMap ℳ = .id) : Decomposition ℳ where
   decompose' := decompose
-  left_inv := FunLike.congr_fun h_left_inv
-  right_inv := FunLike.congr_fun h_right_inv
+  left_inv := DFunLike.congr_fun h_left_inv
+  right_inv := DFunLike.congr_fun h_right_inv
 
 variable [Decomposition ℳ]
 
@@ -294,7 +294,7 @@ theorem decompose_lhom_ext {N} [AddCommMonoid N] [Module R N] ⦃f g : M →ₗ[
   LinearMap.ext <| (decomposeLinearEquiv ℳ).symm.surjective.forall.mpr <|
     suffices f ∘ₗ (decomposeLinearEquiv ℳ).symm
            = (g ∘ₗ (decomposeLinearEquiv ℳ).symm : (⨁ i, ℳ i) →ₗ[R] N) from
-      FunLike.congr_fun this
+      DFunLike.congr_fun this
     linearMap_ext _ fun i => by
       simp_rw [LinearMap.comp_assoc, decomposeLinearEquiv_symm_comp_lof ℳ i, h]

4e861f25

feat(Algebra/DirectSum/Decomposition): degree of a non-zero homogeneous element is unique (#9597)

if $x \in M = \bigoplus M_i$ is not $0$ such that $x \in M_i$ and $x \in M_j$, then $i = j$

b071b57a

Diff

@@ -143,6 +143,10 @@ theorem decompose_of_mem_ne {x : M} {i j : ι} (hx : x ∈ ℳ i) (hij : i ≠ j
   rw [decompose_of_mem _ hx, DirectSum.of_eq_of_ne _ _ _ _ hij, ZeroMemClass.coe_zero]
 #align direct_sum.decompose_of_mem_ne DirectSum.decompose_of_mem_ne
 
+theorem degree_eq_of_mem_mem {x : M} {i j : ι} (hxi : x ∈ ℳ i) (hxj : x ∈ ℳ j) (hx : x ≠ 0) :
+    i = j := by
+  contrapose! hx; rw [← decompose_of_mem_same ℳ hxj, decompose_of_mem_ne ℳ hxi hx]
+
 /-- If `M` is graded by `ι` with degree `i` component `ℳ i`, then it is isomorphic as
 an additive monoid to a direct sum of components. -/
 -- Porting note: deleted [simps] and added the corresponding lemmas by hand

4e861f25

feat(Algebra/DirectSum/Decomposition): some convenience API (#8374)

15ce6b63

Diff

@@ -48,7 +48,10 @@ submonoids `ℳ i` of that `M`, such that the "recomposition" is canonical. This
 works for additive groups and modules.
 
 This is a version of `DirectSum.IsInternal` which comes with a constructive inverse to the
-canonical "recomposition" rather than just a proof that the "recomposition" is bijective. -/
+canonical "recomposition" rather than just a proof that the "recomposition" is bijective.
+
+Often it is easier to construct a term of this type via `Decomposition.ofAddHom` or
+`Decomposition.ofLinearMap`. -/
 class Decomposition where
   decompose' : M → ⨁ i, ℳ i
   left_inv : Function.LeftInverse (DirectSum.coeAddMonoidHom ℳ) decompose'
@@ -63,6 +66,22 @@ instance : Subsingleton (Decomposition ℳ) :=
     congr
     exact Function.LeftInverse.eq_rightInverse xr yl⟩
 
+/-- A convenience method to construct a decomposition from an `AddMonoidHom`, such that the proofs
+of left and right inverse can be constructed via `ext`. -/
+abbrev Decomposition.ofAddHom (decompose : M →+ ⨁ i, ℳ i)
+    (h_left_inv : (DirectSum.coeAddMonoidHom ℳ).comp decompose = .id _)
+    (h_right_inv : decompose.comp (DirectSum.coeAddMonoidHom ℳ) = .id _) : Decomposition ℳ where
+  decompose' := decompose
+  left_inv := FunLike.congr_fun h_left_inv
+  right_inv := FunLike.congr_fun h_right_inv
+
+/-- Noncomputably conjure a decomposition instance from a `DirectSum.IsInternal` proof. -/
+noncomputable def IsInternal.chooseDecomposition (h : IsInternal ℳ) :
+    DirectSum.Decomposition ℳ where
+  decompose' := (Equiv.ofBijective _ h).symm
+  left_inv := (Equiv.ofBijective _ h).right_inv
+  right_inv := (Equiv.ofBijective _ h).left_inv
+
 variable [Decomposition ℳ]
 
 protected theorem Decomposition.isInternal : DirectSum.IsInternal ℳ :=
@@ -230,6 +249,15 @@ variable [DecidableEq ι] [Semiring R] [AddCommMonoid M] [Module R M]
 
 variable (ℳ : ι → Submodule R M)
 
+/-- A convenience method to construct a decomposition from an `LinearMap`, such that the proofs
+of left and right inverse can be constructed via `ext`. -/
+abbrev Decomposition.ofLinearMap (decompose : M →ₗ[R] ⨁ i, ℳ i)
+    (h_left_inv : DirectSum.coeLinearMap ℳ ∘ₗ decompose = .id)
+    (h_right_inv : decompose ∘ₗ DirectSum.coeLinearMap ℳ = .id) : Decomposition ℳ where
+  decompose' := decompose
+  left_inv := FunLike.congr_fun h_left_inv
+  right_inv := FunLike.congr_fun h_right_inv
+
 variable [Decomposition ℳ]
 
 /-- If `M` is graded by `ι` with degree `i` component `ℳ i`, then it is isomorphic as

4e861f25

feat(Algebra/DirectSum/Decomposition): extensionality lemma for maps from a decomposition (#7662)

Two linear maps from a module with a decomposition agree if they agree on every piece.

Also replaces some bad simps lemmas with manual ones.

fca1e12a

Diff

@@ -234,17 +234,38 @@ variable [Decomposition ℳ]
 
 /-- If `M` is graded by `ι` with degree `i` component `ℳ i`, then it is isomorphic as
 a module to a direct sum of components. -/
-@[simps! (config := { fullyApplied := false })]
 def decomposeLinearEquiv : M ≃ₗ[R] ⨁ i, ℳ i :=
   LinearEquiv.symm
     { (decomposeAddEquiv ℳ).symm with map_smul' := map_smul (DirectSum.coeLinearMap ℳ) }
 #align direct_sum.decompose_linear_equiv DirectSum.decomposeLinearEquiv
 
+@[simp] theorem decomposeLinearEquiv_apply (m : M) :
+    decomposeLinearEquiv ℳ m = decompose ℳ m := rfl
+
+@[simp] theorem decomposeLinearEquiv_symm_apply (m : ⨁ i, ℳ i) :
+    (decomposeLinearEquiv ℳ).symm m = (decompose ℳ).symm m := rfl
+
 @[simp]
 theorem decompose_smul (r : R) (x : M) : decompose ℳ (r • x) = r • decompose ℳ x :=
   map_smul (decomposeLinearEquiv ℳ) r x
 #align direct_sum.decompose_smul DirectSum.decompose_smul
 
+@[simp] theorem decomposeLinearEquiv_symm_comp_lof (i : ι) :
+    (decomposeLinearEquiv ℳ).symm ∘ₗ lof R ι (ℳ ·) i = (ℳ i).subtype :=
+  LinearMap.ext <| decompose_symm_of _
+
+/-- Two linear maps from a module with a decomposition agree if they agree on every piece.
+
+Note this cannot be `@[ext]` as `ℳ` cannot be inferred. -/
+theorem decompose_lhom_ext {N} [AddCommMonoid N] [Module R N] ⦃f g : M →ₗ[R] N⦄
+    (h : ∀ i, f ∘ₗ (ℳ i).subtype = g ∘ₗ (ℳ i).subtype) : f = g :=
+  LinearMap.ext <| (decomposeLinearEquiv ℳ).symm.surjective.forall.mpr <|
+    suffices f ∘ₗ (decomposeLinearEquiv ℳ).symm
+           = (g ∘ₗ (decomposeLinearEquiv ℳ).symm : (⨁ i, ℳ i) →ₗ[R] N) from
+      FunLike.congr_fun this
+    linearMap_ext _ fun i => by
+      simp_rw [LinearMap.comp_assoc, decomposeLinearEquiv_symm_comp_lof ℳ i, h]
+
 end Module
 
 end DirectSum

4e861f25

chore: only four spaces for subsequent lines (#7286)

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

0c7d6fa5

Diff

@@ -137,7 +137,7 @@ lemma decomposeAddEquiv_apply (a : M) :
 
 @[simp]
 lemma decomposeAddEquiv_symm_apply (a : ⨁ i, ℳ i) :
-  (decomposeAddEquiv ℳ).symm a = (decompose ℳ).symm a := rfl
+    (decomposeAddEquiv ℳ).symm a = (decompose ℳ).symm a := rfl
 
 @[simp]
 theorem decompose_zero : decompose ℳ (0 : M) = 0 :=

4e861f25

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

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

This has nice performance benefits.

32de3f67

Diff

@@ -31,7 +31,7 @@ bundled homs, but means we don't have to repeat statements for different types o
 -/
 
 
-variable {ι R M σ : Type _}
+variable {ι R M σ : Type*}
 
 open DirectSum BigOperators

4e861f25

chore: fix grammar mistakes (#6121)

a16538af

Diff

@@ -184,7 +184,7 @@ end AddCommMonoid
 
 /-- The `-` in the statements below doesn't resolve without this line.
 
-This seems to a be a problem of synthesized vs inferred typeclasses disagreeing. If we replace
+This seems to be a problem of synthesized vs inferred typeclasses disagreeing. If we replace
 the statement of `decompose_neg` with `@Eq (⨁ i, ℳ i) (decompose ℳ (-x)) (-decompose ℳ x)`
 instead of `decompose ℳ (-x) = -decompose ℳ x`, which forces the typeclasses needed by `⨁ i, ℳ i`
 to be found by unification rather than synthesis, then everything works fine without this

4e861f25

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Jujian Zhang
-
-! This file was ported from Lean 3 source module algebra.direct_sum.decomposition
-! leanprover-community/mathlib commit 4e861f25ba5ceef42ba0712d8ffeb32f38ad6441
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.DirectSum.Module
 import Mathlib.Algebra.Module.Submodule.Basic
 
+#align_import algebra.direct_sum.decomposition from "leanprover-community/mathlib"@"4e861f25ba5ceef42ba0712d8ffeb32f38ad6441"
+
 /-!
 # Decompositions of additive monoids, groups, and modules into direct sums

4e861f25

feat: port Algebra.Module.GradedModule (#4228)

In Algebra.DirectSum.Decomposition, a simps was commented because it was causing a recurrence loop. However, one of the lemma that it generates is needed in this file, so I put the simps back (and fixed the loop)
At the end of the file, the local instance GradedModule.isModule was causing a lot of troubles. (It was in fact marked as a dangerous instance in Mathlib3). I removed it and declared it directly in the only result using it, see this Zulip thread

037038de

Diff

@@ -129,12 +129,19 @@ theorem decompose_of_mem_ne {x : M} {i j : ι} (hx : x ∈ ℳ i) (hij : i ≠ j
 
 /-- If `M` is graded by `ι` with degree `i` component `ℳ i`, then it is isomorphic as
 an additive monoid to a direct sum of components. -/
--- Porting note : this causes a maximum recursion depth
--- @[simps (config := { fullyApplied := false })]
+-- Porting note: deleted [simps] and added the corresponding lemmas by hand
 def decomposeAddEquiv : M ≃+ ⨁ i, ℳ i :=
   AddEquiv.symm { (decompose ℳ).symm with map_add' := map_add (DirectSum.coeAddMonoidHom ℳ) }
 #align direct_sum.decompose_add_equiv DirectSum.decomposeAddEquiv
 
+@[simp]
+lemma decomposeAddEquiv_apply (a : M) :
+    decomposeAddEquiv ℳ a = decompose ℳ a := rfl
+
+@[simp]
+lemma decomposeAddEquiv_symm_apply (a : ⨁ i, ℳ i) :
+  (decomposeAddEquiv ℳ).symm a = (decompose ℳ).symm a := rfl
+
 @[simp]
 theorem decompose_zero : decompose ℳ (0 : M) = 0 :=
   map_zero (decomposeAddEquiv ℳ)

4e861f25

feat port: Algebra.DirectSum.Decomposition (#4081)

A @[simps (config := { fullyApplied := false })] on line 133 is causing a maximum recursion depth so I commented it out with a porting note

870cc2bd

`algebra.direct_sum.decomposition` ⟷ `Mathlib.Algebra.DirectSum.Decomposition`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 424

algebra.direct_sum.decomposition ⟷ Mathlib.Algebra.DirectSum.Decomposition

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 424

`algebra.direct_sum.decomposition` ⟷ `Mathlib.Algebra.DirectSum.Decomposition`