ring_theory.graded_algebra.basic | 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

70fd9563

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

1b0a28e1

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -318,7 +318,7 @@ def GradedRing.projZeroRingHom : A →+* A
               decompose_of_mem_same 𝒜 (show c ∈ 𝒜 0 from (add_eq_zero_iff.mp h).1 ▸ hc),
               decompose_of_mem_same 𝒜 (show c' ∈ 𝒜 0 from (add_eq_zero_iff.mp h).2 ▸ hc')]
           · rw [decompose_of_mem_ne 𝒜 (mul_mem hc hc') h]
-            cases' show i ≠ 0 ∨ j ≠ 0 by rwa [add_eq_zero_iff, not_and_or] at h  with h' h'
+            cases' show i ≠ 0 ∨ j ≠ 0 by rwa [add_eq_zero_iff, not_and_or] at h with h' h'
             · simp only [decompose_of_mem_ne 𝒜 hc h', MulZeroClass.zero_mul]
             · simp only [decompose_of_mem_ne 𝒜 hc' h', MulZeroClass.mul_zero]
       · intro _ _ hd he

1b0a28e1

bump to nightly-2023-10-07-06

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

d191b687

Diff

@@ -289,7 +289,7 @@ open SetLike.GradedMonoid DirectSum
 
 variable [Semiring A] [DecidableEq ι]
 
-variable [CanonicallyOrderedAddMonoid ι]
+variable [CanonicallyOrderedAddCommMonoid ι]
 
 variable [SetLike σ A] [AddSubmonoidClass σ A] (𝒜 : ι → σ) [GradedRing 𝒜]

1b0a28e1

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Kevin Buzzard, Jujian Zhang
 -/
-import Mathbin.Algebra.DirectSum.Algebra
-import Mathbin.Algebra.DirectSum.Decomposition
-import Mathbin.Algebra.DirectSum.Internal
-import Mathbin.Algebra.DirectSum.Ring
+import Algebra.DirectSum.Algebra
+import Algebra.DirectSum.Decomposition
+import Algebra.DirectSum.Internal
+import Algebra.DirectSum.Ring
 
 #align_import ring_theory.graded_algebra.basic from "leanprover-community/mathlib"@"1b0a28e1c93409dbf6d69526863cd9984ef652ce"

1b0a28e1

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -81,7 +81,7 @@ def decomposeRingEquiv : A ≃+* ⨁ i, 𝒜 i :=
   RingEquiv.symm
     {
       (decomposeAddEquiv 𝒜).symm with
-      map_mul' := (coeRingHom 𝒜).map_mul
+      map_mul' := (coeRingHom 𝒜).map_hMul
       map_add' := (coeRingHom 𝒜).map_add }
 #align direct_sum.decompose_ring_equiv DirectSum.decomposeRingEquiv
 -/
@@ -240,8 +240,9 @@ an algebra to a direct sum of components. -/
 @[simps]
 def decomposeAlgEquiv : A ≃ₐ[R] ⨁ i, 𝒜 i :=
   AlgEquiv.symm
-    { (decomposeAddEquiv 𝒜).symm with
-      map_mul' := (coeAlgHom 𝒜).map_mul
+    {
+      (decomposeAddEquiv 𝒜).symm with
+      map_mul' := (coeAlgHom 𝒜).map_hMul
       map_add' := (coeAlgHom 𝒜).map_add
       commutes' := (coeAlgHom 𝒜).commutes }
 #align direct_sum.decompose_alg_equiv DirectSum.decomposeAlgEquiv

1b0a28e1

bump to nightly-2023-08-09-09

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

af9a0040

Diff

@@ -120,7 +120,7 @@ end DirectSum
 #print GradedRing.proj /-
 /-- The projection maps of a graded ring -/
 def GradedRing.proj (i : ι) : A →+ A :=
-  (AddSubmonoidClass.Subtype (𝒜 i)).comp <|
+  (AddSubmonoidClass.subtype (𝒜 i)).comp <|
     (DFinsupp.evalAddMonoidHom i).comp <|
       RingHom.toAddMonoidHom <| RingEquiv.toRingHom <| DirectSum.decomposeRingEquiv 𝒜
 #align graded_ring.proj GradedRing.proj

1b0a28e1

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Kevin Buzzard, Jujian Zhang
-
-! This file was ported from Lean 3 source module ring_theory.graded_algebra.basic
-! leanprover-community/mathlib commit 1b0a28e1c93409dbf6d69526863cd9984ef652ce
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.DirectSum.Algebra
 import Mathbin.Algebra.DirectSum.Decomposition
 import Mathbin.Algebra.DirectSum.Internal
 import Mathbin.Algebra.DirectSum.Ring
 
+#align_import ring_theory.graded_algebra.basic from "leanprover-community/mathlib"@"1b0a28e1c93409dbf6d69526863cd9984ef652ce"
+
 /-!
 # Internally-graded rings and algebras

1b0a28e1

bump to nightly-2023-07-12-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/4e24c4bfcff371c71f7ba22050308aa17815626c

9849f9d1

Diff

@@ -124,7 +124,7 @@ end DirectSum
 /-- The projection maps of a graded ring -/
 def GradedRing.proj (i : ι) : A →+ A :=
   (AddSubmonoidClass.Subtype (𝒜 i)).comp <|
-    (Dfinsupp.evalAddMonoidHom i).comp <|
+    (DFinsupp.evalAddMonoidHom i).comp <|
       RingHom.toAddMonoidHom <| RingEquiv.toRingHom <| DirectSum.decomposeRingEquiv 𝒜
 #align graded_ring.proj GradedRing.proj
 -/
@@ -147,7 +147,7 @@ theorem GradedRing.proj_recompose (a : ⨁ i, 𝒜 i) (i : ι) :
 #print GradedRing.mem_support_iff /-
 theorem GradedRing.mem_support_iff [∀ (i) (x : 𝒜 i), Decidable (x ≠ 0)] (r : A) (i : ι) :
     i ∈ (decompose 𝒜 r).support ↔ GradedRing.proj 𝒜 i r ≠ 0 :=
-  Dfinsupp.mem_support_iff.trans ZeroMemClass.coe_eq_zero.Not.symm
+  DFinsupp.mem_support_iff.trans ZeroMemClass.coe_eq_zero.Not.symm
 #align graded_ring.mem_support_iff GradedRing.mem_support_iff
 -/
 
@@ -257,7 +257,7 @@ open DirectSum
 #print GradedAlgebra.proj /-
 /-- The projection maps of graded algebra-/
 def GradedAlgebra.proj (𝒜 : ι → Submodule R A) [GradedAlgebra 𝒜] (i : ι) : A →ₗ[R] A :=
-  (𝒜 i).Subtype.comp <| (Dfinsupp.lapply i).comp <| (decomposeAlgEquiv 𝒜).toAlgHom.toLinearMap
+  (𝒜 i).Subtype.comp <| (DFinsupp.lapply i).comp <| (decomposeAlgEquiv 𝒜).toAlgHom.toLinearMap
 #align graded_algebra.proj GradedAlgebra.proj
 -/
 
@@ -279,7 +279,7 @@ theorem GradedAlgebra.proj_recompose (a : ⨁ i, 𝒜 i) (i : ι) :
 #print GradedAlgebra.mem_support_iff /-
 theorem GradedAlgebra.mem_support_iff [DecidableEq A] (r : A) (i : ι) :
     i ∈ (decompose 𝒜 r).support ↔ GradedAlgebra.proj 𝒜 i r ≠ 0 :=
-  Dfinsupp.mem_support_iff.trans Submodule.coe_eq_zero.Not.symm
+  DFinsupp.mem_support_iff.trans Submodule.coe_eq_zero.Not.symm
 #align graded_algebra.mem_support_iff GradedAlgebra.mem_support_iff
 -/

1b0a28e1

bump to nightly-2023-06-20-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

9b351f8c

Diff

@@ -228,7 +228,7 @@ def GradedAlgebra.ofAlgHom [SetLike.GradedMonoid 𝒜] (decompose : A →ₐ[R]
   right_inv := by
     suffices : decompose.comp (DirectSum.coeAlgHom 𝒜) = AlgHom.id _ _
     exact AlgHom.congr_fun this
-    ext (i x) : 2
+    ext i x : 2
     exact (decompose.congr_arg <| DirectSum.coeAlgHom_of _ _ _).trans (left_inv i x)
 #align graded_algebra.of_alg_hom GradedAlgebra.ofAlgHom
 -/

1b0a28e1

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -57,8 +57,6 @@ variable [DecidableEq ι] [AddMonoid ι] [CommSemiring R] [Semiring A] [Algebra
 
 variable [SetLike σ A] [AddSubmonoidClass σ A] (𝒜 : ι → σ)
 
-include A
-
 open DirectSum
 
 #print GradedRing /-
@@ -79,6 +77,7 @@ variable [GradedRing 𝒜]
 
 namespace DirectSum
 
+#print DirectSum.decomposeRingEquiv /-
 /-- If `A` is graded by `ι` with degree `i` component `𝒜 i`, then it is isomorphic as
 a ring to a direct sum of components. -/
 def decomposeRingEquiv : A ≃+* ⨁ i, 𝒜 i :=
@@ -88,27 +87,36 @@ def decomposeRingEquiv : A ≃+* ⨁ i, 𝒜 i :=
       map_mul' := (coeRingHom 𝒜).map_mul
       map_add' := (coeRingHom 𝒜).map_add }
 #align direct_sum.decompose_ring_equiv DirectSum.decomposeRingEquiv
+-/
 
+#print DirectSum.decompose_one /-
 @[simp]
 theorem decompose_one : decompose 𝒜 (1 : A) = 1 :=
   map_one (decomposeRingEquiv 𝒜)
 #align direct_sum.decompose_one DirectSum.decompose_one
+-/
 
+#print DirectSum.decompose_symm_one /-
 @[simp]
 theorem decompose_symm_one : (decompose 𝒜).symm 1 = (1 : A) :=
   map_one (decomposeRingEquiv 𝒜).symm
 #align direct_sum.decompose_symm_one DirectSum.decompose_symm_one
+-/
 
+#print DirectSum.decompose_mul /-
 @[simp]
 theorem decompose_mul (x y : A) : decompose 𝒜 (x * y) = decompose 𝒜 x * decompose 𝒜 y :=
   map_mul (decomposeRingEquiv 𝒜) x y
 #align direct_sum.decompose_mul DirectSum.decompose_mul
+-/
 
+#print DirectSum.decompose_symm_mul /-
 @[simp]
 theorem decompose_symm_mul (x y : ⨁ i, 𝒜 i) :
     (decompose 𝒜).symm (x * y) = (decompose 𝒜).symm x * (decompose 𝒜).symm y :=
   map_mul (decomposeRingEquiv 𝒜).symm x y
 #align direct_sum.decompose_symm_mul DirectSum.decompose_symm_mul
+-/
 
 end DirectSum
 
@@ -121,21 +129,27 @@ def GradedRing.proj (i : ι) : A →+ A :=
 #align graded_ring.proj GradedRing.proj
 -/
 
+#print GradedRing.proj_apply /-
 @[simp]
 theorem GradedRing.proj_apply (i : ι) (r : A) :
     GradedRing.proj 𝒜 i r = (decompose 𝒜 r : ⨁ i, 𝒜 i) i :=
   rfl
 #align graded_ring.proj_apply GradedRing.proj_apply
+-/
 
+#print GradedRing.proj_recompose /-
 theorem GradedRing.proj_recompose (a : ⨁ i, 𝒜 i) (i : ι) :
     GradedRing.proj 𝒜 i ((decompose 𝒜).symm a) = (decompose 𝒜).symm (DirectSum.of _ i (a i)) := by
   rw [GradedRing.proj_apply, decompose_symm_of, Equiv.apply_symm_apply]
 #align graded_ring.proj_recompose GradedRing.proj_recompose
+-/
 
+#print GradedRing.mem_support_iff /-
 theorem GradedRing.mem_support_iff [∀ (i) (x : 𝒜 i), Decidable (x ≠ 0)] (r : A) (i : ι) :
     i ∈ (decompose 𝒜 r).support ↔ GradedRing.proj 𝒜 i r ≠ 0 :=
   Dfinsupp.mem_support_iff.trans ZeroMemClass.coe_eq_zero.Not.symm
 #align graded_ring.mem_support_iff GradedRing.mem_support_iff
+-/
 
 end GradedRing
 
@@ -149,27 +163,35 @@ variable {i j : ι}
 
 namespace DirectSum
 
+#print DirectSum.coe_decompose_mul_add_of_left_mem /-
 theorem coe_decompose_mul_add_of_left_mem [AddLeftCancelMonoid ι] [GradedRing 𝒜] {a b : A}
     (a_mem : a ∈ 𝒜 i) : (decompose 𝒜 (a * b) (i + j) : A) = a * decompose 𝒜 b j := by
   lift a to 𝒜 i using a_mem; rw [decompose_mul, decompose_coe, coe_of_mul_apply_add]
 #align direct_sum.coe_decompose_mul_add_of_left_mem DirectSum.coe_decompose_mul_add_of_left_mem
+-/
 
+#print DirectSum.coe_decompose_mul_add_of_right_mem /-
 theorem coe_decompose_mul_add_of_right_mem [AddRightCancelMonoid ι] [GradedRing 𝒜] {a b : A}
     (b_mem : b ∈ 𝒜 j) : (decompose 𝒜 (a * b) (i + j) : A) = decompose 𝒜 a i * b := by
   lift b to 𝒜 j using b_mem; rw [decompose_mul, decompose_coe, coe_mul_of_apply_add]
 #align direct_sum.coe_decompose_mul_add_of_right_mem DirectSum.coe_decompose_mul_add_of_right_mem
+-/
 
+#print DirectSum.decompose_mul_add_left /-
 theorem decompose_mul_add_left [AddLeftCancelMonoid ι] [GradedRing 𝒜] (a : 𝒜 i) {b : A} :
     decompose 𝒜 (↑a * b) (i + j) =
       @GradedMonoid.GMul.mul ι (fun i => 𝒜 i) _ _ _ _ a (decompose 𝒜 b j) :=
   Subtype.ext <| coe_decompose_mul_add_of_left_mem 𝒜 a.2
 #align direct_sum.decompose_mul_add_left DirectSum.decompose_mul_add_left
+-/
 
+#print DirectSum.decompose_mul_add_right /-
 theorem decompose_mul_add_right [AddRightCancelMonoid ι] [GradedRing 𝒜] {a : A} (b : 𝒜 j) :
     decompose 𝒜 (a * ↑b) (i + j) =
       @GradedMonoid.GMul.mul ι (fun i => 𝒜 i) _ _ _ _ (decompose 𝒜 a i) b :=
   Subtype.ext <| coe_decompose_mul_add_of_right_mem 𝒜 b.2
 #align direct_sum.decompose_mul_add_right DirectSum.decompose_mul_add_right
+-/
 
 end DirectSum
 
@@ -239,21 +261,27 @@ def GradedAlgebra.proj (𝒜 : ι → Submodule R A) [GradedAlgebra 𝒜] (i : 
 #align graded_algebra.proj GradedAlgebra.proj
 -/
 
+#print GradedAlgebra.proj_apply /-
 @[simp]
 theorem GradedAlgebra.proj_apply (i : ι) (r : A) :
     GradedAlgebra.proj 𝒜 i r = (decompose 𝒜 r : ⨁ i, 𝒜 i) i :=
   rfl
 #align graded_algebra.proj_apply GradedAlgebra.proj_apply
+-/
 
+#print GradedAlgebra.proj_recompose /-
 theorem GradedAlgebra.proj_recompose (a : ⨁ i, 𝒜 i) (i : ι) :
     GradedAlgebra.proj 𝒜 i ((decompose 𝒜).symm a) = (decompose 𝒜).symm (of _ i (a i)) := by
   rw [GradedAlgebra.proj_apply, decompose_symm_of, Equiv.apply_symm_apply]
 #align graded_algebra.proj_recompose GradedAlgebra.proj_recompose
+-/
 
+#print GradedAlgebra.mem_support_iff /-
 theorem GradedAlgebra.mem_support_iff [DecidableEq A] (r : A) (i : ι) :
     i ∈ (decompose 𝒜 r).support ↔ GradedAlgebra.proj 𝒜 i r ≠ 0 :=
   Dfinsupp.mem_support_iff.trans Submodule.coe_eq_zero.Not.symm
 #align graded_algebra.mem_support_iff GradedAlgebra.mem_support_iff
+-/
 
 end GradedAlgebra
 
@@ -306,37 +334,49 @@ variable {a b : A} {n i : ι}
 
 namespace DirectSum
 
+#print DirectSum.coe_decompose_mul_of_left_mem_of_not_le /-
 theorem coe_decompose_mul_of_left_mem_of_not_le (a_mem : a ∈ 𝒜 i) (h : ¬i ≤ n) :
     (decompose 𝒜 (a * b) n : A) = 0 := by lift a to 𝒜 i using a_mem;
   rwa [decompose_mul, decompose_coe, coe_of_mul_apply_of_not_le]
 #align direct_sum.coe_decompose_mul_of_left_mem_of_not_le DirectSum.coe_decompose_mul_of_left_mem_of_not_le
+-/
 
+#print DirectSum.coe_decompose_mul_of_right_mem_of_not_le /-
 theorem coe_decompose_mul_of_right_mem_of_not_le (b_mem : b ∈ 𝒜 i) (h : ¬i ≤ n) :
     (decompose 𝒜 (a * b) n : A) = 0 := by lift b to 𝒜 i using b_mem;
   rwa [decompose_mul, decompose_coe, coe_mul_of_apply_of_not_le]
 #align direct_sum.coe_decompose_mul_of_right_mem_of_not_le DirectSum.coe_decompose_mul_of_right_mem_of_not_le
+-/
 
 variable [Sub ι] [OrderedSub ι] [ContravariantClass ι ι (· + ·) (· ≤ ·)]
 
+#print DirectSum.coe_decompose_mul_of_left_mem_of_le /-
 theorem coe_decompose_mul_of_left_mem_of_le (a_mem : a ∈ 𝒜 i) (h : i ≤ n) :
     (decompose 𝒜 (a * b) n : A) = a * decompose 𝒜 b (n - i) := by lift a to 𝒜 i using a_mem;
   rwa [decompose_mul, decompose_coe, coe_of_mul_apply_of_le]
 #align direct_sum.coe_decompose_mul_of_left_mem_of_le DirectSum.coe_decompose_mul_of_left_mem_of_le
+-/
 
+#print DirectSum.coe_decompose_mul_of_right_mem_of_le /-
 theorem coe_decompose_mul_of_right_mem_of_le (b_mem : b ∈ 𝒜 i) (h : i ≤ n) :
     (decompose 𝒜 (a * b) n : A) = decompose 𝒜 a (n - i) * b := by lift b to 𝒜 i using b_mem;
   rwa [decompose_mul, decompose_coe, coe_mul_of_apply_of_le]
 #align direct_sum.coe_decompose_mul_of_right_mem_of_le DirectSum.coe_decompose_mul_of_right_mem_of_le
+-/
 
+#print DirectSum.coe_decompose_mul_of_left_mem /-
 theorem coe_decompose_mul_of_left_mem (n) [Decidable (i ≤ n)] (a_mem : a ∈ 𝒜 i) :
     (decompose 𝒜 (a * b) n : A) = if i ≤ n then a * decompose 𝒜 b (n - i) else 0 := by
   lift a to 𝒜 i using a_mem; rwa [decompose_mul, decompose_coe, coe_of_mul_apply]
 #align direct_sum.coe_decompose_mul_of_left_mem DirectSum.coe_decompose_mul_of_left_mem
+-/
 
+#print DirectSum.coe_decompose_mul_of_right_mem /-
 theorem coe_decompose_mul_of_right_mem (n) [Decidable (i ≤ n)] (b_mem : b ∈ 𝒜 i) :
     (decompose 𝒜 (a * b) n : A) = if i ≤ n then decompose 𝒜 a (n - i) * b else 0 := by
   lift b to 𝒜 i using b_mem; rwa [decompose_mul, decompose_coe, coe_mul_of_apply]
 #align direct_sum.coe_decompose_mul_of_right_mem DirectSum.coe_decompose_mul_of_right_mem
+-/
 
 end DirectSum

1b0a28e1

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -292,7 +292,7 @@ def GradedRing.projZeroRingHom : A →+* A
               decompose_of_mem_same 𝒜 (show c ∈ 𝒜 0 from (add_eq_zero_iff.mp h).1 ▸ hc),
               decompose_of_mem_same 𝒜 (show c' ∈ 𝒜 0 from (add_eq_zero_iff.mp h).2 ▸ hc')]
           · rw [decompose_of_mem_ne 𝒜 (mul_mem hc hc') h]
-            cases' show i ≠ 0 ∨ j ≠ 0 by rwa [add_eq_zero_iff, not_and_or] at h with h' h'
+            cases' show i ≠ 0 ∨ j ≠ 0 by rwa [add_eq_zero_iff, not_and_or] at h  with h' h'
             · simp only [decompose_of_mem_ne 𝒜 hc h', MulZeroClass.zero_mul]
             · simp only [decompose_of_mem_ne 𝒜 hc' h', MulZeroClass.mul_zero]
       · intro _ _ hd he

1b0a28e1

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -47,7 +47,7 @@ graded algebra, graded ring, graded semiring, decomposition
 -/
 
 
-open DirectSum BigOperators
+open scoped DirectSum BigOperators
 
 variable {ι R A σ : Type _}

1b0a28e1

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -79,12 +79,6 @@ variable [GradedRing 𝒜]
 
 namespace DirectSum
 
-/- warning: direct_sum.decompose_ring_equiv -> DirectSum.decomposeRingEquiv is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u3, u2} σ A] [_inst_7 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜], RingEquiv.{u2, max u1 u2} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))) (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))) (Distrib.toHasMul.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.nonUnitalNonAssocSemiring.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i) (SetLike.gnonUnitalNonAssocSemiring.{u1, u3, u2} ι σ A (fun (a : ι) (b : ι) => _inst_1 a b) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)) _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) (DirectSum.decomposeRingEquiv._proof_1.{u1, u2, u3} ι A σ _inst_1 _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))))) (Distrib.toHasAdd.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.nonUnitalNonAssocSemiring.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i) (SetLike.gnonUnitalNonAssocSemiring.{u1, u3, u2} ι σ A (fun (a : ι) (b : ι) => _inst_1 a b) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)) _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) (DirectSum.decomposeRingEquiv._proof_1.{u1, u2, u3} ι A σ _inst_1 _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)))))
-but is expected to have type
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u3, u2} σ A] [_inst_7 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜], RingEquiv.{u2, max u2 u1} A (DirectSum.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u3} A σ (SetLike.instMembership.{u3, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u3} A σ (SetLike.instMembership.{u3, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.instNonUnitalNonAssocSemiringDirectSum.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u3} A σ (SetLike.instMembership.{u3, u2} σ A _inst_6) x (𝒜 i))) (AddZeroClass.toAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i) (SetLike.gnonUnitalNonAssocSemiring.{u1, u3, u2} ι σ A (AddZeroClass.toAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)) _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedMul.{u1, u2, u3} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8))))) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))) (Distrib.toAdd.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u3} A σ (SetLike.instMembership.{u3, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u3} A σ (SetLike.instMembership.{u3, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.instNonUnitalNonAssocSemiringDirectSum.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u3} A σ (SetLike.instMembership.{u3, u2} σ A _inst_6) x (𝒜 i))) (AddZeroClass.toAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i) (SetLike.gnonUnitalNonAssocSemiring.{u1, u3, u2} ι σ A (AddZeroClass.toAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)) _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedMul.{u1, u2, u3} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8))))))
-Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_ring_equiv DirectSum.decomposeRingEquivₓ'. -/
 /-- If `A` is graded by `ι` with degree `i` component `𝒜 i`, then it is isomorphic as
 a ring to a direct sum of components. -/
 def decomposeRingEquiv : A ≃+* ⨁ i, 𝒜 i :=
@@ -95,33 +89,21 @@ def decomposeRingEquiv : A ≃+* ⨁ i, 𝒜 i :=
       map_add' := (coeRingHom 𝒜).map_add }
 #align direct_sum.decompose_ring_equiv DirectSum.decomposeRingEquiv
 
-/- warning: direct_sum.decompose_one -> DirectSum.decompose_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_one DirectSum.decompose_oneₓ'. -/
 @[simp]
 theorem decompose_one : decompose 𝒜 (1 : A) = 1 :=
   map_one (decomposeRingEquiv 𝒜)
 #align direct_sum.decompose_one DirectSum.decompose_one
 
-/- warning: direct_sum.decompose_symm_one -> DirectSum.decompose_symm_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_one DirectSum.decompose_symm_oneₓ'. -/
 @[simp]
 theorem decompose_symm_one : (decompose 𝒜).symm 1 = (1 : A) :=
   map_one (decomposeRingEquiv 𝒜).symm
 #align direct_sum.decompose_symm_one DirectSum.decompose_symm_one
 
-/- warning: direct_sum.decompose_mul -> DirectSum.decompose_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_mul DirectSum.decompose_mulₓ'. -/
 @[simp]
 theorem decompose_mul (x y : A) : decompose 𝒜 (x * y) = decompose 𝒜 x * decompose 𝒜 y :=
   map_mul (decomposeRingEquiv 𝒜) x y
 #align direct_sum.decompose_mul DirectSum.decompose_mul
 
-/- warning: direct_sum.decompose_symm_mul -> DirectSum.decompose_symm_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_mul DirectSum.decompose_symm_mulₓ'. -/
 @[simp]
 theorem decompose_symm_mul (x y : ⨁ i, 𝒜 i) :
     (decompose 𝒜).symm (x * y) = (decompose 𝒜).symm x * (decompose 𝒜).symm y :=
@@ -139,26 +121,17 @@ def GradedRing.proj (i : ι) : A →+ A :=
 #align graded_ring.proj GradedRing.proj
 -/
 
-/- warning: graded_ring.proj_apply -> GradedRing.proj_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align graded_ring.proj_apply GradedRing.proj_applyₓ'. -/
 @[simp]
 theorem GradedRing.proj_apply (i : ι) (r : A) :
     GradedRing.proj 𝒜 i r = (decompose 𝒜 r : ⨁ i, 𝒜 i) i :=
   rfl
 #align graded_ring.proj_apply GradedRing.proj_apply
 
-/- warning: graded_ring.proj_recompose -> GradedRing.proj_recompose is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align graded_ring.proj_recompose GradedRing.proj_recomposeₓ'. -/
 theorem GradedRing.proj_recompose (a : ⨁ i, 𝒜 i) (i : ι) :
     GradedRing.proj 𝒜 i ((decompose 𝒜).symm a) = (decompose 𝒜).symm (DirectSum.of _ i (a i)) := by
   rw [GradedRing.proj_apply, decompose_symm_of, Equiv.apply_symm_apply]
 #align graded_ring.proj_recompose GradedRing.proj_recompose
 
-/- warning: graded_ring.mem_support_iff -> GradedRing.mem_support_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align graded_ring.mem_support_iff GradedRing.mem_support_iffₓ'. -/
 theorem GradedRing.mem_support_iff [∀ (i) (x : 𝒜 i), Decidable (x ≠ 0)] (r : A) (i : ι) :
     i ∈ (decompose 𝒜 r).support ↔ GradedRing.proj 𝒜 i r ≠ 0 :=
   Dfinsupp.mem_support_iff.trans ZeroMemClass.coe_eq_zero.Not.symm
@@ -176,34 +149,22 @@ variable {i j : ι}
 
 namespace DirectSum
 
-/- warning: direct_sum.coe_decompose_mul_add_of_left_mem -> DirectSum.coe_decompose_mul_add_of_left_mem is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_add_of_left_mem DirectSum.coe_decompose_mul_add_of_left_memₓ'. -/
 theorem coe_decompose_mul_add_of_left_mem [AddLeftCancelMonoid ι] [GradedRing 𝒜] {a b : A}
     (a_mem : a ∈ 𝒜 i) : (decompose 𝒜 (a * b) (i + j) : A) = a * decompose 𝒜 b j := by
   lift a to 𝒜 i using a_mem; rw [decompose_mul, decompose_coe, coe_of_mul_apply_add]
 #align direct_sum.coe_decompose_mul_add_of_left_mem DirectSum.coe_decompose_mul_add_of_left_mem
 
-/- warning: direct_sum.coe_decompose_mul_add_of_right_mem -> DirectSum.coe_decompose_mul_add_of_right_mem is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_add_of_right_mem DirectSum.coe_decompose_mul_add_of_right_memₓ'. -/
 theorem coe_decompose_mul_add_of_right_mem [AddRightCancelMonoid ι] [GradedRing 𝒜] {a b : A}
     (b_mem : b ∈ 𝒜 j) : (decompose 𝒜 (a * b) (i + j) : A) = decompose 𝒜 a i * b := by
   lift b to 𝒜 j using b_mem; rw [decompose_mul, decompose_coe, coe_mul_of_apply_add]
 #align direct_sum.coe_decompose_mul_add_of_right_mem DirectSum.coe_decompose_mul_add_of_right_mem
 
-/- warning: direct_sum.decompose_mul_add_left -> DirectSum.decompose_mul_add_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_mul_add_left DirectSum.decompose_mul_add_leftₓ'. -/
 theorem decompose_mul_add_left [AddLeftCancelMonoid ι] [GradedRing 𝒜] (a : 𝒜 i) {b : A} :
     decompose 𝒜 (↑a * b) (i + j) =
       @GradedMonoid.GMul.mul ι (fun i => 𝒜 i) _ _ _ _ a (decompose 𝒜 b j) :=
   Subtype.ext <| coe_decompose_mul_add_of_left_mem 𝒜 a.2
 #align direct_sum.decompose_mul_add_left DirectSum.decompose_mul_add_left
 
-/- warning: direct_sum.decompose_mul_add_right -> DirectSum.decompose_mul_add_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_mul_add_right DirectSum.decompose_mul_add_rightₓ'. -/
 theorem decompose_mul_add_right [AddRightCancelMonoid ι] [GradedRing 𝒜] {a : A} (b : 𝒜 j) :
     decompose 𝒜 (a * ↑b) (i + j) =
       @GradedMonoid.GMul.mul ι (fun i => 𝒜 i) _ _ _ _ (decompose 𝒜 a i) b :=
@@ -278,26 +239,17 @@ def GradedAlgebra.proj (𝒜 : ι → Submodule R A) [GradedAlgebra 𝒜] (i : 
 #align graded_algebra.proj GradedAlgebra.proj
 -/
 
-/- warning: graded_algebra.proj_apply -> GradedAlgebra.proj_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align graded_algebra.proj_apply GradedAlgebra.proj_applyₓ'. -/
 @[simp]
 theorem GradedAlgebra.proj_apply (i : ι) (r : A) :
     GradedAlgebra.proj 𝒜 i r = (decompose 𝒜 r : ⨁ i, 𝒜 i) i :=
   rfl
 #align graded_algebra.proj_apply GradedAlgebra.proj_apply
 
-/- warning: graded_algebra.proj_recompose -> GradedAlgebra.proj_recompose is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align graded_algebra.proj_recompose GradedAlgebra.proj_recomposeₓ'. -/
 theorem GradedAlgebra.proj_recompose (a : ⨁ i, 𝒜 i) (i : ι) :
     GradedAlgebra.proj 𝒜 i ((decompose 𝒜).symm a) = (decompose 𝒜).symm (of _ i (a i)) := by
   rw [GradedAlgebra.proj_apply, decompose_symm_of, Equiv.apply_symm_apply]
 #align graded_algebra.proj_recompose GradedAlgebra.proj_recompose
 
-/- warning: graded_algebra.mem_support_iff -> GradedAlgebra.mem_support_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align graded_algebra.mem_support_iff GradedAlgebra.mem_support_iffₓ'. -/
 theorem GradedAlgebra.mem_support_iff [DecidableEq A] (r : A) (i : ι) :
     i ∈ (decompose 𝒜 r).support ↔ GradedAlgebra.proj 𝒜 i r ≠ 0 :=
   Dfinsupp.mem_support_iff.trans Submodule.coe_eq_zero.Not.symm
@@ -354,17 +306,11 @@ variable {a b : A} {n i : ι}
 
 namespace DirectSum
 
-/- warning: direct_sum.coe_decompose_mul_of_left_mem_of_not_le -> DirectSum.coe_decompose_mul_of_left_mem_of_not_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_left_mem_of_not_le DirectSum.coe_decompose_mul_of_left_mem_of_not_leₓ'. -/
 theorem coe_decompose_mul_of_left_mem_of_not_le (a_mem : a ∈ 𝒜 i) (h : ¬i ≤ n) :
     (decompose 𝒜 (a * b) n : A) = 0 := by lift a to 𝒜 i using a_mem;
   rwa [decompose_mul, decompose_coe, coe_of_mul_apply_of_not_le]
 #align direct_sum.coe_decompose_mul_of_left_mem_of_not_le DirectSum.coe_decompose_mul_of_left_mem_of_not_le
 
-/- warning: direct_sum.coe_decompose_mul_of_right_mem_of_not_le -> DirectSum.coe_decompose_mul_of_right_mem_of_not_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_right_mem_of_not_le DirectSum.coe_decompose_mul_of_right_mem_of_not_leₓ'. -/
 theorem coe_decompose_mul_of_right_mem_of_not_le (b_mem : b ∈ 𝒜 i) (h : ¬i ≤ n) :
     (decompose 𝒜 (a * b) n : A) = 0 := by lift b to 𝒜 i using b_mem;
   rwa [decompose_mul, decompose_coe, coe_mul_of_apply_of_not_le]
@@ -372,33 +318,21 @@ theorem coe_decompose_mul_of_right_mem_of_not_le (b_mem : b ∈ 𝒜 i) (h : ¬i
 
 variable [Sub ι] [OrderedSub ι] [ContravariantClass ι ι (· + ·) (· ≤ ·)]
 
-/- warning: direct_sum.coe_decompose_mul_of_left_mem_of_le -> DirectSum.coe_decompose_mul_of_left_mem_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_left_mem_of_le DirectSum.coe_decompose_mul_of_left_mem_of_leₓ'. -/
 theorem coe_decompose_mul_of_left_mem_of_le (a_mem : a ∈ 𝒜 i) (h : i ≤ n) :
     (decompose 𝒜 (a * b) n : A) = a * decompose 𝒜 b (n - i) := by lift a to 𝒜 i using a_mem;
   rwa [decompose_mul, decompose_coe, coe_of_mul_apply_of_le]
 #align direct_sum.coe_decompose_mul_of_left_mem_of_le DirectSum.coe_decompose_mul_of_left_mem_of_le
 
-/- warning: direct_sum.coe_decompose_mul_of_right_mem_of_le -> DirectSum.coe_decompose_mul_of_right_mem_of_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_right_mem_of_le DirectSum.coe_decompose_mul_of_right_mem_of_leₓ'. -/
 theorem coe_decompose_mul_of_right_mem_of_le (b_mem : b ∈ 𝒜 i) (h : i ≤ n) :
     (decompose 𝒜 (a * b) n : A) = decompose 𝒜 a (n - i) * b := by lift b to 𝒜 i using b_mem;
   rwa [decompose_mul, decompose_coe, coe_mul_of_apply_of_le]
 #align direct_sum.coe_decompose_mul_of_right_mem_of_le DirectSum.coe_decompose_mul_of_right_mem_of_le
 
-/- warning: direct_sum.coe_decompose_mul_of_left_mem -> DirectSum.coe_decompose_mul_of_left_mem is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_left_mem DirectSum.coe_decompose_mul_of_left_memₓ'. -/
 theorem coe_decompose_mul_of_left_mem (n) [Decidable (i ≤ n)] (a_mem : a ∈ 𝒜 i) :
     (decompose 𝒜 (a * b) n : A) = if i ≤ n then a * decompose 𝒜 b (n - i) else 0 := by
   lift a to 𝒜 i using a_mem; rwa [decompose_mul, decompose_coe, coe_of_mul_apply]
 #align direct_sum.coe_decompose_mul_of_left_mem DirectSum.coe_decompose_mul_of_left_mem
 
-/- warning: direct_sum.coe_decompose_mul_of_right_mem -> DirectSum.coe_decompose_mul_of_right_mem is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_right_mem DirectSum.coe_decompose_mul_of_right_memₓ'. -/
 theorem coe_decompose_mul_of_right_mem (n) [Decidable (i ≤ n)] (b_mem : b ∈ 𝒜 i) :
     (decompose 𝒜 (a * b) n : A) = if i ≤ n then decompose 𝒜 a (n - i) * b else 0 := by
   lift b to 𝒜 i using b_mem; rwa [decompose_mul, decompose_coe, coe_mul_of_apply]

1b0a28e1

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -180,20 +180,16 @@ namespace DirectSum
 <too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_add_of_left_mem DirectSum.coe_decompose_mul_add_of_left_memₓ'. -/
 theorem coe_decompose_mul_add_of_left_mem [AddLeftCancelMonoid ι] [GradedRing 𝒜] {a b : A}
-    (a_mem : a ∈ 𝒜 i) : (decompose 𝒜 (a * b) (i + j) : A) = a * decompose 𝒜 b j :=
-  by
-  lift a to 𝒜 i using a_mem
-  rw [decompose_mul, decompose_coe, coe_of_mul_apply_add]
+    (a_mem : a ∈ 𝒜 i) : (decompose 𝒜 (a * b) (i + j) : A) = a * decompose 𝒜 b j := by
+  lift a to 𝒜 i using a_mem; rw [decompose_mul, decompose_coe, coe_of_mul_apply_add]
 #align direct_sum.coe_decompose_mul_add_of_left_mem DirectSum.coe_decompose_mul_add_of_left_mem
 
 /- warning: direct_sum.coe_decompose_mul_add_of_right_mem -> DirectSum.coe_decompose_mul_add_of_right_mem is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_add_of_right_mem DirectSum.coe_decompose_mul_add_of_right_memₓ'. -/
 theorem coe_decompose_mul_add_of_right_mem [AddRightCancelMonoid ι] [GradedRing 𝒜] {a b : A}
-    (b_mem : b ∈ 𝒜 j) : (decompose 𝒜 (a * b) (i + j) : A) = decompose 𝒜 a i * b :=
-  by
-  lift b to 𝒜 j using b_mem
-  rw [decompose_mul, decompose_coe, coe_mul_of_apply_add]
+    (b_mem : b ∈ 𝒜 j) : (decompose 𝒜 (a * b) (i + j) : A) = decompose 𝒜 a i * b := by
+  lift b to 𝒜 j using b_mem; rw [decompose_mul, decompose_coe, coe_mul_of_apply_add]
 #align direct_sum.coe_decompose_mul_add_of_right_mem DirectSum.coe_decompose_mul_add_of_right_mem
 
 /- warning: direct_sum.decompose_mul_add_left -> DirectSum.decompose_mul_add_left is a dubious translation:
@@ -328,12 +324,8 @@ def GradedRing.projZeroRingHom : A →+* A
     where
   toFun a := decompose 𝒜 a 0
   map_one' := decompose_of_mem_same 𝒜 one_mem
-  map_zero' := by
-    rw [decompose_zero]
-    rfl
-  map_add' _ _ := by
-    rw [decompose_add]
-    rfl
+  map_zero' := by rw [decompose_zero]; rfl
+  map_add' _ _ := by rw [decompose_add]; rfl
   map_mul' := by
     refine' DirectSum.Decomposition.inductionOn 𝒜 (fun x => _) _ _
     · simp only [MulZeroClass.zero_mul, decompose_zero, zero_apply, ZeroMemClass.coe_zero]
@@ -366,9 +358,7 @@ namespace DirectSum
 <too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_left_mem_of_not_le DirectSum.coe_decompose_mul_of_left_mem_of_not_leₓ'. -/
 theorem coe_decompose_mul_of_left_mem_of_not_le (a_mem : a ∈ 𝒜 i) (h : ¬i ≤ n) :
-    (decompose 𝒜 (a * b) n : A) = 0 :=
-  by
-  lift a to 𝒜 i using a_mem
+    (decompose 𝒜 (a * b) n : A) = 0 := by lift a to 𝒜 i using a_mem;
   rwa [decompose_mul, decompose_coe, coe_of_mul_apply_of_not_le]
 #align direct_sum.coe_decompose_mul_of_left_mem_of_not_le DirectSum.coe_decompose_mul_of_left_mem_of_not_le
 
@@ -376,9 +366,7 @@ theorem coe_decompose_mul_of_left_mem_of_not_le (a_mem : a ∈ 𝒜 i) (h : ¬i
 <too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_right_mem_of_not_le DirectSum.coe_decompose_mul_of_right_mem_of_not_leₓ'. -/
 theorem coe_decompose_mul_of_right_mem_of_not_le (b_mem : b ∈ 𝒜 i) (h : ¬i ≤ n) :
-    (decompose 𝒜 (a * b) n : A) = 0 :=
-  by
-  lift b to 𝒜 i using b_mem
+    (decompose 𝒜 (a * b) n : A) = 0 := by lift b to 𝒜 i using b_mem;
   rwa [decompose_mul, decompose_coe, coe_mul_of_apply_of_not_le]
 #align direct_sum.coe_decompose_mul_of_right_mem_of_not_le DirectSum.coe_decompose_mul_of_right_mem_of_not_le
 
@@ -388,9 +376,7 @@ variable [Sub ι] [OrderedSub ι] [ContravariantClass ι ι (· + ·) (· ≤ ·
 <too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_left_mem_of_le DirectSum.coe_decompose_mul_of_left_mem_of_leₓ'. -/
 theorem coe_decompose_mul_of_left_mem_of_le (a_mem : a ∈ 𝒜 i) (h : i ≤ n) :
-    (decompose 𝒜 (a * b) n : A) = a * decompose 𝒜 b (n - i) :=
-  by
-  lift a to 𝒜 i using a_mem
+    (decompose 𝒜 (a * b) n : A) = a * decompose 𝒜 b (n - i) := by lift a to 𝒜 i using a_mem;
   rwa [decompose_mul, decompose_coe, coe_of_mul_apply_of_le]
 #align direct_sum.coe_decompose_mul_of_left_mem_of_le DirectSum.coe_decompose_mul_of_left_mem_of_le
 
@@ -398,9 +384,7 @@ theorem coe_decompose_mul_of_left_mem_of_le (a_mem : a ∈ 𝒜 i) (h : i ≤ n)
 <too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_right_mem_of_le DirectSum.coe_decompose_mul_of_right_mem_of_leₓ'. -/
 theorem coe_decompose_mul_of_right_mem_of_le (b_mem : b ∈ 𝒜 i) (h : i ≤ n) :
-    (decompose 𝒜 (a * b) n : A) = decompose 𝒜 a (n - i) * b :=
-  by
-  lift b to 𝒜 i using b_mem
+    (decompose 𝒜 (a * b) n : A) = decompose 𝒜 a (n - i) * b := by lift b to 𝒜 i using b_mem;
   rwa [decompose_mul, decompose_coe, coe_mul_of_apply_of_le]
 #align direct_sum.coe_decompose_mul_of_right_mem_of_le DirectSum.coe_decompose_mul_of_right_mem_of_le
 
@@ -408,20 +392,16 @@ theorem coe_decompose_mul_of_right_mem_of_le (b_mem : b ∈ 𝒜 i) (h : i ≤ n
 <too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_left_mem DirectSum.coe_decompose_mul_of_left_memₓ'. -/
 theorem coe_decompose_mul_of_left_mem (n) [Decidable (i ≤ n)] (a_mem : a ∈ 𝒜 i) :
-    (decompose 𝒜 (a * b) n : A) = if i ≤ n then a * decompose 𝒜 b (n - i) else 0 :=
-  by
-  lift a to 𝒜 i using a_mem
-  rwa [decompose_mul, decompose_coe, coe_of_mul_apply]
+    (decompose 𝒜 (a * b) n : A) = if i ≤ n then a * decompose 𝒜 b (n - i) else 0 := by
+  lift a to 𝒜 i using a_mem; rwa [decompose_mul, decompose_coe, coe_of_mul_apply]
 #align direct_sum.coe_decompose_mul_of_left_mem DirectSum.coe_decompose_mul_of_left_mem
 
 /- warning: direct_sum.coe_decompose_mul_of_right_mem -> DirectSum.coe_decompose_mul_of_right_mem is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_right_mem DirectSum.coe_decompose_mul_of_right_memₓ'. -/
 theorem coe_decompose_mul_of_right_mem (n) [Decidable (i ≤ n)] (b_mem : b ∈ 𝒜 i) :
-    (decompose 𝒜 (a * b) n : A) = if i ≤ n then decompose 𝒜 a (n - i) * b else 0 :=
-  by
-  lift b to 𝒜 i using b_mem
-  rwa [decompose_mul, decompose_coe, coe_mul_of_apply]
+    (decompose 𝒜 (a * b) n : A) = if i ≤ n then decompose 𝒜 a (n - i) * b else 0 := by
+  lift b to 𝒜 i using b_mem; rwa [decompose_mul, decompose_coe, coe_mul_of_apply]
 #align direct_sum.coe_decompose_mul_of_right_mem DirectSum.coe_decompose_mul_of_right_mem
 
 end DirectSum

1b0a28e1

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -96,10 +96,7 @@ def decomposeRingEquiv : A ≃+* ⨁ i, 𝒜 i :=
 #align direct_sum.decompose_ring_equiv DirectSum.decomposeRingEquiv
 
 /- warning: direct_sum.decompose_one -> DirectSum.decompose_one is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u3, u2} σ A] [_inst_7 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜], 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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))))) (OfNat.ofNat.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) 1 (OfNat.mk.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) 1 (One.one.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.hasOne.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddZeroClass.toHasZero.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (SetLike.gOne.{u1, u2, u3} ι A σ _inst_6 (MulOneClass.toHasOne.{u2} A (Monoid.toMulOneClass.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)))) (AddZeroClass.toHasZero.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.to_gradedOne.{u1, u2, u3} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.to_gradedMonoid.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))))))
-but is expected to have type
-  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddMonoid.{u3} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u1, u2} σ A] [_inst_7 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜], Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_4)))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_4)))) (OfNat.ofNat.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_4)))) 1 (One.toOfNat1.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_4)))) (DirectSum.instOneDirectSum.{u3, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (AddMonoid.toZero.{u3} ι _inst_2) (SetLike.gOne.{u3, u2, u1} ι A σ _inst_6 (Semiring.toOne.{u2} A _inst_4) (AddMonoid.toZero.{u3} ι _inst_2) (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedOne.{u3, u2, u1} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_one DirectSum.decompose_oneₓ'. -/
 @[simp]
 theorem decompose_one : decompose 𝒜 (1 : A) = 1 :=
@@ -107,10 +104,7 @@ theorem decompose_one : decompose 𝒜 (1 : A) = 1 :=
 #align direct_sum.decompose_one DirectSum.decompose_one
 
 /- warning: direct_sum.decompose_symm_one -> DirectSum.decompose_symm_one is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u3, u2} σ A] [_inst_7 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜], Eq.{succ u2} A (coeFn.{max 1 (max (succ (max u1 u2)) (succ u2)) (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) => (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) -> A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) (OfNat.ofNat.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) 1 (OfNat.mk.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) 1 (One.one.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.hasOne.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddZeroClass.toHasZero.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (SetLike.gOne.{u1, u2, u3} ι A σ _inst_6 (MulOneClass.toHasOne.{u2} A (Monoid.toMulOneClass.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)))) (AddZeroClass.toHasZero.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.to_gradedOne.{u1, u2, u3} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.to_gradedMonoid.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))))))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))))
-but is expected to have type
-  forall {ι : Type.{u2}} {A : Type.{u3}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} ι] [_inst_2 : AddMonoid.{u2} ι] [_inst_4 : Semiring.{u3} A] [_inst_6 : SetLike.{u1, u3} σ A] [_inst_7 : AddSubmonoidClass.{u1, u3} σ A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u2, u3, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜], Eq.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) (OfNat.ofNat.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) 1 (One.toOfNat1.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.instOneDirectSum.{u2, u3} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (AddMonoid.toZero.{u2} ι _inst_2) (SetLike.gOne.{u2, u3, u1} ι A σ _inst_6 (Semiring.toOne.{u3} A _inst_4) (AddMonoid.toZero.{u2} ι _inst_2) (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedOne.{u2, u3, u1} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u2, u3, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 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} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (fun (_x : DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u3), succ u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u3, max (succ u2) (succ u3)} A (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u2, u3, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u2, u3, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) (OfNat.ofNat.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) 1 (One.toOfNat1.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.instOneDirectSum.{u2, u3} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (AddMonoid.toZero.{u2} ι _inst_2) (SetLike.gOne.{u2, u3, u1} ι A σ _inst_6 (Semiring.toOne.{u3} A _inst_4) (AddMonoid.toZero.{u2} ι _inst_2) (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedOne.{u2, u3, u1} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u2, u3, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))))) (OfNat.ofNat.{u3} A 1 (One.toOfNat1.{u3} A (Semiring.toOne.{u3} A _inst_4)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_one DirectSum.decompose_symm_oneₓ'. -/
 @[simp]
 theorem decompose_symm_one : (decompose 𝒜).symm 1 = (1 : A) :=
@@ -118,10 +112,7 @@ theorem decompose_symm_one : (decompose 𝒜).symm 1 = (1 : A) :=
 #align direct_sum.decompose_symm_one DirectSum.decompose_symm_one
 
 /- warning: direct_sum.decompose_mul -> DirectSum.decompose_mul is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u3, u2} σ A] [_inst_7 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] (x : A) (y : A), 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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) x y)) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (instHMul.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (Distrib.toHasMul.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.nonUnitalNonAssocSemiring.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)) (SetLike.gnonUnitalNonAssocSemiring.{u1, u3, u2} ι σ A (fun (a : ι) (b : ι) => _inst_1 a b) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)) _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.to_gradedMul.{u1, u2, u3} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.to_gradedMonoid.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8))))))) (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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) x) (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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) y))
-but is expected to have type
-  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddMonoid.{u3} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u1, u2} σ A] [_inst_7 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] (x : A) (y : A), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))) x y)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))) x y)) (HMul.hMul.{max u3 u2, max u3 u2, max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) x) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) y) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) x) (instHMul.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) x) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) x) (DirectSum.instNonUnitalNonAssocSemiringDirectSum.{u3, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι _inst_2)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)) (SetLike.gnonUnitalNonAssocSemiring.{u3, u1, u2} ι σ A (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)) _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedMul.{u3, u2, u1} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8)))))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) x) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) y))
+<too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_mul DirectSum.decompose_mulₓ'. -/
 @[simp]
 theorem decompose_mul (x y : A) : decompose 𝒜 (x * y) = decompose 𝒜 x * decompose 𝒜 y :=
@@ -129,10 +120,7 @@ theorem decompose_mul (x y : A) : decompose 𝒜 (x * y) = decompose 𝒜 x * de
 #align direct_sum.decompose_mul DirectSum.decompose_mul
 
 /- warning: direct_sum.decompose_symm_mul -> DirectSum.decompose_symm_mul is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u3, u2} σ A] [_inst_7 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] (x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (y : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)), Eq.{succ u2} A (coeFn.{max 1 (max (succ (max u1 u2)) (succ u2)) (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) => (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) -> A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (instHMul.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (Distrib.toHasMul.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.nonUnitalNonAssocSemiring.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)) (SetLike.gnonUnitalNonAssocSemiring.{u1, u3, u2} ι σ A (fun (a : ι) (b : ι) => _inst_1 a b) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)) _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.to_gradedMul.{u1, u2, u3} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.to_gradedMonoid.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8))))))) x y)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (coeFn.{max 1 (max (succ (max u1 u2)) (succ u2)) (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) => (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) -> A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) x) (coeFn.{max 1 (max (succ (max u1 u2)) (succ u2)) (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) => (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) -> A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) y))
-but is expected to have type
-  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddMonoid.{u3} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u1, u2} σ A] [_inst_7 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] (x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (y : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) (HMul.hMul.{max u3 u2, max u3 u2, max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (instHMul.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.instNonUnitalNonAssocSemiringDirectSum.{u3, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι _inst_2)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i) (SetLike.gnonUnitalNonAssocSemiring.{u3, u1, u2} ι σ A (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)) _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedMul.{u3, u2, u1} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8)))))) x y)) (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} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (fun (_x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) (HMul.hMul.{max u3 u2, max u3 u2, max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (instHMul.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.instNonUnitalNonAssocSemiringDirectSum.{u3, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι _inst_2)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i) (SetLike.gnonUnitalNonAssocSemiring.{u3, u1, u2} ι σ A (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)) _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedMul.{u3, u2, u1} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8)))))) x y)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) x) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) y) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) x) (instHMul.{u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) x) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) x) _inst_4)))) (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} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (fun (_x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) x) (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} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (fun (_x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) y))
+<too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_mul DirectSum.decompose_symm_mulₓ'. -/
 @[simp]
 theorem decompose_symm_mul (x y : ⨁ i, 𝒜 i) :
@@ -152,10 +140,7 @@ def GradedRing.proj (i : ι) : A →+ A :=
 -/
 
 /- warning: graded_ring.proj_apply -> GradedRing.proj_apply is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u3, u2} σ A] [_inst_7 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] (i : ι) (r : A), Eq.{succ u2} A (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (fun (_x : AddMonoidHom.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) => A -> A) (AddMonoidHom.hasCoeToFun.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (GradedRing.proj.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8 i) r) ((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 A _inst_6) (𝒜 i)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_6) x (𝒜 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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) r) i))
-but is expected to have type
-  forall {ι : Type.{u2}} {A : Type.{u3}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} ι] [_inst_2 : AddMonoid.{u2} ι] [_inst_4 : Semiring.{u3} A] [_inst_6 : SetLike.{u1, u3} σ A] [_inst_7 : AddSubmonoidClass.{u1, u3} σ A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u2, u3, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] (i : ι) (r : A), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) r) (FunLike.coe.{succ u3, succ u3, succ u3} (AddMonoidHom.{u3, u3} A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) _x) (AddHomClass.toFunLike.{u3, u3, u3} (AddMonoidHom.{u3, u3} A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) A A (AddZeroClass.toAdd.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) (AddZeroClass.toAdd.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) (AddMonoidHomClass.toAddHomClass.{u3, u3, u3} (AddMonoidHom.{u3, u3} A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoidHom.addMonoidHomClass.{u3, u3} A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))))) (GradedRing.proj.{u2, u3, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8 i) r) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u1, u3} σ A _inst_6 (𝒜 i))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Dfinsupp.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (Equiv.{succ u3, max (succ u3) (succ u2)} A (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u2) (succ u3)} A (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u2, u3, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u2, u3, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) r) i))
+<too large>
 Case conversion may be inaccurate. Consider using '#align graded_ring.proj_apply GradedRing.proj_applyₓ'. -/
 @[simp]
 theorem GradedRing.proj_apply (i : ι) (r : A) :
@@ -164,10 +149,7 @@ theorem GradedRing.proj_apply (i : ι) (r : A) :
 #align graded_ring.proj_apply GradedRing.proj_apply
 
 /- warning: graded_ring.proj_recompose -> GradedRing.proj_recompose is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u3, u2} σ A] [_inst_7 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] (a : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (i : ι), Eq.{succ u2} A (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (fun (_x : AddMonoidHom.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) => A -> A) (AddMonoidHom.hasCoeToFun.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (GradedRing.proj.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8 i) (coeFn.{max 1 (max (succ (max u1 u2)) (succ u2)) (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) => (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) -> A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) a)) (coeFn.{max 1 (max (succ (max u1 u2)) (succ u2)) (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) => (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) -> A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (AddMonoidHom.{u2, max u1 u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (AddMonoid.toAddZeroClass.{u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddCommMonoid.toAddMonoid.{u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (AddMonoid.toAddZeroClass.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (AddCommMonoid.toAddMonoid.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.addCommMonoid.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))))) (fun (_x : AddMonoidHom.{u2, max u1 u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (AddMonoid.toAddZeroClass.{u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddCommMonoid.toAddMonoid.{u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (AddMonoid.toAddZeroClass.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (AddCommMonoid.toAddMonoid.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.addCommMonoid.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))))) => (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (AddMonoidHom.hasCoeToFun.{u2, max u1 u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (AddMonoid.toAddZeroClass.{u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddCommMonoid.toAddMonoid.{u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (AddMonoid.toAddZeroClass.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (AddCommMonoid.toAddMonoid.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.addCommMonoid.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))))) (DirectSum.of.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)) 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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) a i)))
-but is expected to have type
-  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddMonoid.{u3} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u1, u2} σ A] [_inst_7 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] (a : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) (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} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (fun (a : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) a) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (AddMonoidHom.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) _x) (AddHomClass.toFunLike.{u2, u2, u2} (AddMonoidHom.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) A A (AddZeroClass.toAdd.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (AddZeroClass.toAdd.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (AddMonoidHomClass.toAddHomClass.{u2, u2, u2} (AddMonoidHom.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoidHom.addMonoidHomClass.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))))) (GradedRing.proj.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8 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} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (fun (_x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) a)) (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} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (fun (_x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (AddMonoidHom.{u2, max u2 u3} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))))) ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (_x : (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) => DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) _x) (AddHomClass.toFunLike.{max u3 u2, u2, max u3 u2} (AddMonoidHom.{u2, max u2 u3} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))))) ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddZeroClass.toAdd.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)))) (AddZeroClass.toAdd.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))))) (AddMonoidHomClass.toAddHomClass.{max u3 u2, u2, max u3 u2} (AddMonoidHom.{u2, max u2 u3} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))))) ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)))) (AddMonoidHom.addMonoidHomClass.{u2, max u3 u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))))))) (DirectSum.of.{u3, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i) i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) i) ((fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) i) ((fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i) i))) i)) a i)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align graded_ring.proj_recompose GradedRing.proj_recomposeₓ'. -/
 theorem GradedRing.proj_recompose (a : ⨁ i, 𝒜 i) (i : ι) :
     GradedRing.proj 𝒜 i ((decompose 𝒜).symm a) = (decompose 𝒜).symm (DirectSum.of _ i (a i)) := by
@@ -175,10 +157,7 @@ theorem GradedRing.proj_recompose (a : ⨁ i, 𝒜 i) (i : ι) :
 #align graded_ring.proj_recompose GradedRing.proj_recompose
 
 /- warning: graded_ring.mem_support_iff -> GradedRing.mem_support_iff is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u3, u2} σ A] [_inst_7 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] [_inst_9 : forall (i : ι) (x : coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)), Decidable (Ne.{succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) x (OfNat.ofNat.{u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) 0 (OfNat.mk.{u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) 0 (Zero.zero.{u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (ZeroMemClass.zero.{u3, u2} σ A _inst_6 (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (AddSubmonoidClass.to_zeroMemClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6 _inst_7) (𝒜 i))))))] (r : A) (i : ι), Iff (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i (Dfinsupp.support.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) i) (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => AddZeroClass.toHasZero.{u2} ((fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) i) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)) i)))) (fun (i : ι) (x : coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) => _inst_9 i x) (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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) r))) (Ne.{succ u2} A (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (fun (_x : AddMonoidHom.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) => A -> A) (AddMonoidHom.hasCoeToFun.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (GradedRing.proj.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8 i) r) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))))))
-but is expected to have type
-  forall {ι : Type.{u1}} {A : Type.{u3}} {σ : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u3} A] [_inst_6 : SetLike.{u2, u3} σ A] [_inst_7 : AddSubmonoidClass.{u2, u3} σ A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] [_inst_9 : forall (i : ι) (x : Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))), Decidable (Ne.{succ u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))) x (OfNat.ofNat.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))) 0 (Zero.toOfNat0.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))) (ZeroMemClass.zero.{u2, u3} σ A _inst_6 (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_4)) (AddSubmonoidClass.toZeroMemClass.{u2, u3} σ A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) _inst_6 _inst_7) (𝒜 i)))))] (r : A) (i : ι), Iff (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i (Dfinsupp.support.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 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} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)) i))) (fun (i : ι) (x : Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))) => _inst_9 i x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, max (succ u1) (succ u3)} (Equiv.{succ u3, max (succ u3) (succ u1)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) r))) (Ne.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) r) (FunLike.coe.{succ u3, succ u3, succ u3} (AddMonoidHom.{u3, u3} A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) _x) (AddHomClass.toFunLike.{u3, u3, u3} (AddMonoidHom.{u3, u3} A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) A A (AddZeroClass.toAdd.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) (AddZeroClass.toAdd.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) (AddMonoidHomClass.toAddHomClass.{u3, u3, u3} (AddMonoidHom.{u3, u3} A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoidHom.addMonoidHomClass.{u3, u3} A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))))) (GradedRing.proj.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8 i) r) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) r) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) r) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) r) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) r) _inst_4)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align graded_ring.mem_support_iff GradedRing.mem_support_iffₓ'. -/
 theorem GradedRing.mem_support_iff [∀ (i) (x : 𝒜 i), Decidable (x ≠ 0)] (r : A) (i : ι) :
     i ∈ (decompose 𝒜 r).support ↔ GradedRing.proj 𝒜 i r ≠ 0 :=
@@ -198,10 +177,7 @@ variable {i j : ι}
 namespace DirectSum
 
 /- warning: direct_sum.coe_decompose_mul_add_of_left_mem -> DirectSum.coe_decompose_mul_add_of_left_mem is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : Semiring.{u2} A] [_inst_3 : SetLike.{u3, u2} σ A] [_inst_4 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) _inst_3] (𝒜 : ι -> σ) {i : ι} {j : ι} [_inst_5 : AddLeftCancelMonoid.{u1} ι] [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜] {a : A} {b : A}, (Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_3) a (𝒜 i)) -> (Eq.{succ u2} A ((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 A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_3) x (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))))))) (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 A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) a b)) (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) a ((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 A _inst_3) (𝒜 j)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 j)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 j)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 j)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_3) x (𝒜 j)))))) (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 A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) b) j))))
-but is expected to have type
-  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} A] [_inst_3 : SetLike.{u1, u2} σ A] [_inst_4 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) _inst_3] (𝒜 : ι -> σ) {i : ι} {j : ι} [_inst_5 : AddLeftCancelMonoid.{u3} ι] [_inst_6 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜] {a : A} {b : A}, (Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) a (𝒜 i)) -> (Eq.{succ u2} A (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_3 (𝒜 (HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5)))) i j)))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a b)) (HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5)))) i j))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_3 (𝒜 j))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) b) j))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_add_of_left_mem DirectSum.coe_decompose_mul_add_of_left_memₓ'. -/
 theorem coe_decompose_mul_add_of_left_mem [AddLeftCancelMonoid ι] [GradedRing 𝒜] {a b : A}
     (a_mem : a ∈ 𝒜 i) : (decompose 𝒜 (a * b) (i + j) : A) = a * decompose 𝒜 b j :=
@@ -211,10 +187,7 @@ theorem coe_decompose_mul_add_of_left_mem [AddLeftCancelMonoid ι] [GradedRing 
 #align direct_sum.coe_decompose_mul_add_of_left_mem DirectSum.coe_decompose_mul_add_of_left_mem
 
 /- warning: direct_sum.coe_decompose_mul_add_of_right_mem -> DirectSum.coe_decompose_mul_add_of_right_mem is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : Semiring.{u2} A] [_inst_3 : SetLike.{u3, u2} σ A] [_inst_4 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) _inst_3] (𝒜 : ι -> σ) {i : ι} {j : ι} [_inst_5 : AddRightCancelMonoid.{u1} ι] [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜] {a : A} {b : A}, (Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_3) b (𝒜 j)) -> (Eq.{succ u2} A ((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 A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_3) x (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))))))) (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 A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) a b)) (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) ((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 A _inst_3) (𝒜 i)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_3) x (𝒜 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 A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) a) i)) b))
-but is expected to have type
-  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} A] [_inst_3 : SetLike.{u1, u2} σ A] [_inst_4 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) _inst_3] (𝒜 : ι -> σ) {i : ι} {j : ι} [_inst_5 : AddRightCancelMonoid.{u3} ι] [_inst_6 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜] {a : A} {b : A}, (Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) b (𝒜 j)) -> (Eq.{succ u2} A (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_3 (𝒜 (HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5)))) i j)))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a b)) (HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5)))) i j))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_3 (𝒜 i))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) a) i)) b))
+<too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_add_of_right_mem DirectSum.coe_decompose_mul_add_of_right_memₓ'. -/
 theorem coe_decompose_mul_add_of_right_mem [AddRightCancelMonoid ι] [GradedRing 𝒜] {a b : A}
     (b_mem : b ∈ 𝒜 j) : (decompose 𝒜 (a * b) (i + j) : A) = decompose 𝒜 a i * b :=
@@ -224,10 +197,7 @@ theorem coe_decompose_mul_add_of_right_mem [AddRightCancelMonoid ι] [GradedRing
 #align direct_sum.coe_decompose_mul_add_of_right_mem DirectSum.coe_decompose_mul_add_of_right_mem
 
 /- warning: direct_sum.decompose_mul_add_left -> DirectSum.decompose_mul_add_left is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : Semiring.{u2} A] [_inst_3 : SetLike.{u3, u2} σ A] [_inst_4 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) _inst_3] (𝒜 : ι -> σ) {i : ι} {j : ι} [_inst_5 : AddLeftCancelMonoid.{u1} ι] [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜] (a : coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) {b : A}, Eq.{succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) (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 A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) ((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 A _inst_3) (𝒜 i)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_3) x (𝒜 i)))))) a) b)) (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j)) (GradedMonoid.GMul.mul.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5))) (SetLike.gMul.{u1, u2, u3} ι A σ _inst_3 (MulOneClass.toHasMul.{u2} A (Monoid.toMulOneClass.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5))) (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.to_gradedMul.{u1, u2, u3} ι A σ _inst_3 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5) (fun (i : ι) => 𝒜 i) (GradedRing.to_gradedMonoid.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 (fun (i : ι) => 𝒜 i) _inst_6))) i j a (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 A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) b) j))
-but is expected to have type
-  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} A] [_inst_3 : SetLike.{u1, u2} σ A] [_inst_4 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) _inst_3] (𝒜 : ι -> σ) {i : ι} {j : ι} [_inst_5 : AddLeftCancelMonoid.{u3} ι] [_inst_6 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜] (a : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) {b : A}, Eq.{succ u2} ((fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5)))) i j)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_3 (𝒜 i))) a) b)) (HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5)))) i j)) (GradedMonoid.GMul.mul.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5))) (SetLike.gMul.{u3, u2, u1} ι A σ _inst_3 (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5))) (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedMul.{u3, u2, u1} ι A σ _inst_3 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5) (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 (fun (i : ι) => 𝒜 i) _inst_6))) i j a (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) b) j))
+<too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_mul_add_left DirectSum.decompose_mul_add_leftₓ'. -/
 theorem decompose_mul_add_left [AddLeftCancelMonoid ι] [GradedRing 𝒜] (a : 𝒜 i) {b : A} :
     decompose 𝒜 (↑a * b) (i + j) =
@@ -236,10 +206,7 @@ theorem decompose_mul_add_left [AddLeftCancelMonoid ι] [GradedRing 𝒜] (a : 
 #align direct_sum.decompose_mul_add_left DirectSum.decompose_mul_add_left
 
 /- warning: direct_sum.decompose_mul_add_right -> DirectSum.decompose_mul_add_right is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : Semiring.{u2} A] [_inst_3 : SetLike.{u3, u2} σ A] [_inst_4 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) _inst_3] (𝒜 : ι -> σ) {i : ι} {j : ι} [_inst_5 : AddRightCancelMonoid.{u1} ι] [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜] {a : A} (b : coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 j)), Eq.{succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) (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 A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) a ((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 A _inst_3) (𝒜 j)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 j)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 j)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 j)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_3) x (𝒜 j)))))) b))) (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j)) (GradedMonoid.GMul.mul.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5))) (SetLike.gMul.{u1, u2, u3} ι A σ _inst_3 (MulOneClass.toHasMul.{u2} A (Monoid.toMulOneClass.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5))) (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.to_gradedMul.{u1, u2, u3} ι A σ _inst_3 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5) (fun (i : ι) => 𝒜 i) (GradedRing.to_gradedMonoid.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 (fun (i : ι) => 𝒜 i) _inst_6))) i j (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 A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) a) i) b)
-but is expected to have type
-  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} A] [_inst_3 : SetLike.{u1, u2} σ A] [_inst_4 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) _inst_3] (𝒜 : ι -> σ) {i : ι} {j : ι} [_inst_5 : AddRightCancelMonoid.{u3} ι] [_inst_6 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜] {a : A} (b : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 j))), Eq.{succ u2} ((fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5)))) i j)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_3 (𝒜 j))) b))) (HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5)))) i j)) (GradedMonoid.GMul.mul.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5))) (SetLike.gMul.{u3, u2, u1} ι A σ _inst_3 (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5))) (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedMul.{u3, u2, u1} ι A σ _inst_3 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5) (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 (fun (i : ι) => 𝒜 i) _inst_6))) i j (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) a) i) b)
+<too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_mul_add_right DirectSum.decompose_mul_add_rightₓ'. -/
 theorem decompose_mul_add_right [AddRightCancelMonoid ι] [GradedRing 𝒜] {a : A} (b : 𝒜 j) :
     decompose 𝒜 (a * ↑b) (i + j) =
@@ -316,10 +283,7 @@ def GradedAlgebra.proj (𝒜 : ι → Submodule R A) [GradedAlgebra 𝒜] (i : 
 -/
 
 /- warning: graded_algebra.proj_apply -> GradedAlgebra.proj_apply is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_3 : CommSemiring.{u2} R] [_inst_4 : Semiring.{u3} A] [_inst_5 : Algebra.{u2, u3} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] (i : ι) (r : A), Eq.{succ u3} A (coeFn.{succ u3, succ u3} (LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (_x : LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) => A -> A) (LinearMap.hasCoeToFun.{u2, u2, u3, u3} R R A A (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3)))) (GradedAlgebra.proj.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 i) r) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) A (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) A (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) A (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) A (coeSubtype.{succ u3} A (fun (x : A) => Membership.Mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i)))))) (coeFn.{succ (max u1 u3), max (succ u1) (succ u3)} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (fun (_x : DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (coeFn.{max 1 (max (succ u3) (succ (max u1 u3))) (succ (max u1 u3)) (succ u3), max (succ u3) (succ (max u1 u3))} (Equiv.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (fun (_x : Equiv.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) => A -> (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (Equiv.hasCoeToFun.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (DirectSum.decompose.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6)) r) i))
-but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_3 : CommSemiring.{u2} R] [_inst_4 : Semiring.{u3} A] [_inst_5 : Algebra.{u2, u3} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] (i : ι) (r : A), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) r) (FunLike.coe.{succ u3, succ u3, succ u3} (LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u3} R R A A (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3)))) (GradedAlgebra.proj.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 i) r) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 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} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 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)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (DirectSum.decompose.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6)) r) i))
+<too large>
 Case conversion may be inaccurate. Consider using '#align graded_algebra.proj_apply GradedAlgebra.proj_applyₓ'. -/
 @[simp]
 theorem GradedAlgebra.proj_apply (i : ι) (r : A) :
@@ -328,10 +292,7 @@ theorem GradedAlgebra.proj_apply (i : ι) (r : A) :
 #align graded_algebra.proj_apply GradedAlgebra.proj_apply
 
 /- warning: graded_algebra.proj_recompose -> GradedAlgebra.proj_recompose is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_3 : CommSemiring.{u2} R] [_inst_4 : Semiring.{u3} A] [_inst_5 : Algebra.{u2, u3} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] (a : DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u3} ι (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (i : ι), Eq.{succ u3} A (coeFn.{succ u3, succ u3} (LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (_x : LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) => A -> A) (LinearMap.hasCoeToFun.{u2, u2, u3, u3} R R A A (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3)))) (GradedAlgebra.proj.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 i) (coeFn.{max 1 (max (succ (max u1 u3)) (succ u3)) (succ u3) (succ (max u1 u3)), max (succ (max u1 u3)) (succ u3)} (Equiv.{succ (max u1 u3), succ u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (fun (_x : Equiv.{succ (max u1 u3), succ u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) => (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) -> A) (Equiv.hasCoeToFun.{succ (max u1 u3), succ u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (Equiv.symm.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.decompose.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6))) a)) (coeFn.{max 1 (max (succ (max u1 u3)) (succ u3)) (succ u3) (succ (max u1 u3)), max (succ (max u1 u3)) (succ u3)} (Equiv.{succ (max u1 u3), succ u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (fun (_x : Equiv.{succ (max u1 u3), succ u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) => (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) -> A) (Equiv.hasCoeToFun.{succ (max u1 u3), succ u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (Equiv.symm.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.decompose.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6))) (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ u3) (succ (max u1 u3))} (AddMonoidHom.{u3, max u1 u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (AddMonoid.toAddZeroClass.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (AddCommMonoid.toAddMonoid.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.addCommMonoid.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))))) (fun (_x : AddMonoidHom.{u3, max u1 u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (AddMonoid.toAddZeroClass.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (AddCommMonoid.toAddMonoid.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.addCommMonoid.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))))) => (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) -> (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (AddMonoidHom.hasCoeToFun.{u3, max u1 u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (AddMonoid.toAddZeroClass.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (AddCommMonoid.toAddMonoid.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.addCommMonoid.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))))) (DirectSum.of.{u1, u3} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i) (coeFn.{succ (max u1 u3), max (succ u1) (succ u3)} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u3} ι (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (fun (_x : DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u3} ι (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) => forall (i : ι), coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u3} ι (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) a i)))
-but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddMonoid.{u3} ι] [_inst_3 : CommSemiring.{u1} R] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u3, u1, u2} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] (a : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) (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} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (fun (a : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => A) a) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.decompose.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6))) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_3) (CommSemiring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R A A (CommSemiring.toSemiring.{u1} R _inst_3) (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3)))) (GradedAlgebra.proj.{u3, u1, u2} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 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} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (fun (_x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.decompose.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6))) a)) (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} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (fun (_x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.decompose.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (AddMonoidHom.{u2, max u2 u3} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))) ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (_x : (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) => DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) _x) (AddHomClass.toFunLike.{max u3 u2, u2, max u3 u2} (AddMonoidHom.{u2, max u2 u3} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))) ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddZeroClass.toAdd.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)))) (AddZeroClass.toAdd.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))) (AddMonoidHomClass.toAddHomClass.{max u3 u2, u2, max u3 u2} (AddMonoidHom.{u2, max u2 u3} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))) ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)))) (AddMonoidHom.addMonoidHomClass.{u2, max u3 u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))))) (DirectSum.of.{u3, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i) i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i) i))) i)) a i)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align graded_algebra.proj_recompose GradedAlgebra.proj_recomposeₓ'. -/
 theorem GradedAlgebra.proj_recompose (a : ⨁ i, 𝒜 i) (i : ι) :
     GradedAlgebra.proj 𝒜 i ((decompose 𝒜).symm a) = (decompose 𝒜).symm (of _ i (a i)) := by
@@ -339,10 +300,7 @@ theorem GradedAlgebra.proj_recompose (a : ⨁ i, 𝒜 i) (i : ι) :
 #align graded_algebra.proj_recompose GradedAlgebra.proj_recompose
 
 /- warning: graded_algebra.mem_support_iff -> GradedAlgebra.mem_support_iff is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_3 : CommSemiring.{u2} R] [_inst_4 : Semiring.{u3} A] [_inst_5 : Algebra.{u2, u3} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] [_inst_7 : DecidableEq.{succ u3} A] (r : A) (i : ι), Iff (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i (Dfinsupp.support.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i)))) (fun (i : ι) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) => Ne.decidable.{succ u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (fun (a : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (b : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) => Subtype.decidableEq.{u3} A (fun (x : A) => Membership.Mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i)) (fun (a : A) (b : A) => _inst_7 a b) a b) x (OfNat.ofNat.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) 0 (OfNat.mk.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) 0 (Zero.zero.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (AddZeroClass.toHasZero.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i)))))))) (coeFn.{max 1 (max (succ u3) (succ (max u1 u3))) (succ (max u1 u3)) (succ u3), max (succ u3) (succ (max u1 u3))} (Equiv.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (fun (_x : Equiv.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) => A -> (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (Equiv.hasCoeToFun.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (DirectSum.decompose.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6)) r))) (Ne.{succ u3} A (coeFn.{succ u3, succ u3} (LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (_x : LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) => A -> A) (LinearMap.hasCoeToFun.{u2, u2, u3, u3} R R A A (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3)))) (GradedAlgebra.proj.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 i) r) (OfNat.ofNat.{u3} A 0 (OfNat.mk.{u3} A 0 (Zero.zero.{u3} A (MulZeroClass.toHasZero.{u3} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))))))
-but is expected to have type
-  forall {ι : Type.{u2}} {R : Type.{u1}} {A : Type.{u3}} [_inst_1 : DecidableEq.{succ u2} ι] [_inst_2 : AddMonoid.{u2} ι] [_inst_3 : CommSemiring.{u1} R] [_inst_4 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u3} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u2, u1, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] [_inst_7 : DecidableEq.{succ u3} A] (r : A) (i : ι), Iff (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i (Dfinsupp.support.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 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} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i))) (fun (i : ι) (x : Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) => instDecidableNot (Eq.{succ u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) x (OfNat.ofNat.{u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) 0 (Zero.toOfNat0.{u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i)))))) (Subtype.instDecidableEqSubtype.{u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i)) (fun (a : A) (b : A) => _inst_7 a b) x (OfNat.ofNat.{u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) 0 (Zero.toOfNat0.{u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i))))))) (FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (Equiv.{succ u3, max (succ u3) (succ u2)} A (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u2) (succ u3)} A (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (DirectSum.decompose.{u2, u3, u3} ι A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u2, u3, u3} ι A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6)) r))) (Ne.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) r) (FunLike.coe.{succ u3, succ u3, succ u3} (LinearMap.{u1, u1, u3, u3} R R (CommSemiring.toSemiring.{u1} R _inst_3) (CommSemiring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u3} R R A A (CommSemiring.toSemiring.{u1} R _inst_3) (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3)))) (GradedAlgebra.proj.{u2, u1, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 i) r) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) r) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) r) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) r) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) r) _inst_4)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align graded_algebra.mem_support_iff GradedAlgebra.mem_support_iffₓ'. -/
 theorem GradedAlgebra.mem_support_iff [DecidableEq A] (r : A) (i : ι) :
     i ∈ (decompose 𝒜 r).support ↔ GradedAlgebra.proj 𝒜 i r ≠ 0 :=
@@ -405,10 +363,7 @@ variable {a b : A} {n i : ι}
 namespace DirectSum
 
 /- warning: direct_sum.coe_decompose_mul_of_left_mem_of_not_le -> DirectSum.coe_decompose_mul_of_left_mem_of_not_le is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : Semiring.{u2} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u3, u2} σ A] [_inst_5 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {n : ι} {i : ι}, (Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) a (𝒜 i)) -> (Not (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n)) -> (Eq.{succ u2} A ((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 A _inst_4) (𝒜 n)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 n)))))) (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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) a b)) n)) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))))))
-but is expected to have type
-  forall {ι : Type.{u1}} {A : Type.{u3}} {σ : Type.{u2}} [_inst_1 : Semiring.{u3} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u2, u3} σ A] [_inst_5 : AddSubmonoidClass.{u2, u3} σ A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {n : ι} {i : ι}, (Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) a (𝒜 i)) -> (Not (LE.le.{u1} ι (Preorder.toLE.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n)) -> (Eq.{succ u3} A (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u2, u3} σ A _inst_4 (𝒜 n))) (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} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u3, u3, u3} A A A (instHMul.{u3} A (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1)))) a b)) n)) (OfNat.ofNat.{u3} A 0 (Zero.toOfNat0.{u3} A (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_1)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_left_mem_of_not_le DirectSum.coe_decompose_mul_of_left_mem_of_not_leₓ'. -/
 theorem coe_decompose_mul_of_left_mem_of_not_le (a_mem : a ∈ 𝒜 i) (h : ¬i ≤ n) :
     (decompose 𝒜 (a * b) n : A) = 0 :=
@@ -418,10 +373,7 @@ theorem coe_decompose_mul_of_left_mem_of_not_le (a_mem : a ∈ 𝒜 i) (h : ¬i
 #align direct_sum.coe_decompose_mul_of_left_mem_of_not_le DirectSum.coe_decompose_mul_of_left_mem_of_not_le
 
 /- warning: direct_sum.coe_decompose_mul_of_right_mem_of_not_le -> DirectSum.coe_decompose_mul_of_right_mem_of_not_le is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : Semiring.{u2} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u3, u2} σ A] [_inst_5 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {n : ι} {i : ι}, (Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) b (𝒜 i)) -> (Not (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n)) -> (Eq.{succ u2} A ((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 A _inst_4) (𝒜 n)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 n)))))) (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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) a b)) n)) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))))))
-but is expected to have type
-  forall {ι : Type.{u1}} {A : Type.{u3}} {σ : Type.{u2}} [_inst_1 : Semiring.{u3} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u2, u3} σ A] [_inst_5 : AddSubmonoidClass.{u2, u3} σ A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {n : ι} {i : ι}, (Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) b (𝒜 i)) -> (Not (LE.le.{u1} ι (Preorder.toLE.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n)) -> (Eq.{succ u3} A (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u2, u3} σ A _inst_4 (𝒜 n))) (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} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u3, u3, u3} A A A (instHMul.{u3} A (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1)))) a b)) n)) (OfNat.ofNat.{u3} A 0 (Zero.toOfNat0.{u3} A (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_1)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_right_mem_of_not_le DirectSum.coe_decompose_mul_of_right_mem_of_not_leₓ'. -/
 theorem coe_decompose_mul_of_right_mem_of_not_le (b_mem : b ∈ 𝒜 i) (h : ¬i ≤ n) :
     (decompose 𝒜 (a * b) n : A) = 0 :=
@@ -433,10 +385,7 @@ theorem coe_decompose_mul_of_right_mem_of_not_le (b_mem : b ∈ 𝒜 i) (h : ¬i
 variable [Sub ι] [OrderedSub ι] [ContravariantClass ι ι (· + ·) (· ≤ ·)]
 
 /- warning: direct_sum.coe_decompose_mul_of_left_mem_of_le -> DirectSum.coe_decompose_mul_of_left_mem_of_le is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : Semiring.{u2} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u3, u2} σ A] [_inst_5 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {n : ι} {i : ι} [_inst_7 : Sub.{u1} ι] [_inst_8 : OrderedSub.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))) _inst_7] [_inst_9 : ContravariantClass.{u1, u1} ι ι (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))))) (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))))], (Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) a (𝒜 i)) -> (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n) -> (Eq.{succ u2} A ((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 A _inst_4) (𝒜 n)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 n)))))) (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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) a b)) n)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) a ((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 A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n 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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) b) (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i)))))
-but is expected to have type
-  forall {ι : Type.{u1}} {A : Type.{u3}} {σ : Type.{u2}} [_inst_1 : Semiring.{u3} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u2, u3} σ A] [_inst_5 : AddSubmonoidClass.{u2, u3} σ A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {n : ι} {i : ι} [_inst_7 : Sub.{u1} ι] [_inst_8 : OrderedSub.{u1} ι (Preorder.toLE.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) (AddZeroClass.toAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))) _inst_7] [_inst_9 : ContravariantClass.{u1, u1} ι ι (fun (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3010 : ι) (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3012 : ι) => HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))))) x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3010 x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3012) (fun (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3025 : ι) (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3027 : ι) => LE.le.{u1} ι (Preorder.toLE.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3025 x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3027)], (Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) a (𝒜 i)) -> (LE.le.{u1} ι (Preorder.toLE.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n) -> (Eq.{succ u3} A (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u2, u3} σ A _inst_4 (𝒜 n))) (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} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u3, u3, u3} A A A (instHMul.{u3} A (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1)))) a b)) n)) (HMul.hMul.{u3, u3, u3} A A A (instHMul.{u3} A (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1)))) a (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u2, u3} σ A _inst_4 (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n 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} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) b) (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_left_mem_of_le DirectSum.coe_decompose_mul_of_left_mem_of_leₓ'. -/
 theorem coe_decompose_mul_of_left_mem_of_le (a_mem : a ∈ 𝒜 i) (h : i ≤ n) :
     (decompose 𝒜 (a * b) n : A) = a * decompose 𝒜 b (n - i) :=
@@ -446,10 +395,7 @@ theorem coe_decompose_mul_of_left_mem_of_le (a_mem : a ∈ 𝒜 i) (h : i ≤ n)
 #align direct_sum.coe_decompose_mul_of_left_mem_of_le DirectSum.coe_decompose_mul_of_left_mem_of_le
 
 /- warning: direct_sum.coe_decompose_mul_of_right_mem_of_le -> DirectSum.coe_decompose_mul_of_right_mem_of_le is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : Semiring.{u2} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u3, u2} σ A] [_inst_5 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {n : ι} {i : ι} [_inst_7 : Sub.{u1} ι] [_inst_8 : OrderedSub.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))) _inst_7] [_inst_9 : ContravariantClass.{u1, u1} ι ι (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))))) (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))))], (Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) b (𝒜 i)) -> (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n) -> (Eq.{succ u2} A ((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 A _inst_4) (𝒜 n)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 n)))))) (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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) a b)) n)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) ((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 A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n 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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) a) (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) b))
-but is expected to have type
-  forall {ι : Type.{u1}} {A : Type.{u3}} {σ : Type.{u2}} [_inst_1 : Semiring.{u3} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u2, u3} σ A] [_inst_5 : AddSubmonoidClass.{u2, u3} σ A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {n : ι} {i : ι} [_inst_7 : Sub.{u1} ι] [_inst_8 : OrderedSub.{u1} ι (Preorder.toLE.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) (AddZeroClass.toAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))) _inst_7] [_inst_9 : ContravariantClass.{u1, u1} ι ι (fun (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3183 : ι) (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3185 : ι) => HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))))) x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3183 x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3185) (fun (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3198 : ι) (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3200 : ι) => LE.le.{u1} ι (Preorder.toLE.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3198 x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3200)], (Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) b (𝒜 i)) -> (LE.le.{u1} ι (Preorder.toLE.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n) -> (Eq.{succ u3} A (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u2, u3} σ A _inst_4 (𝒜 n))) (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} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u3, u3, u3} A A A (instHMul.{u3} A (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1)))) a b)) n)) (HMul.hMul.{u3, u3, u3} A A A (instHMul.{u3} A (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1)))) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u2, u3} σ A _inst_4 (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n 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} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) a) (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) b))
+<too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_right_mem_of_le DirectSum.coe_decompose_mul_of_right_mem_of_leₓ'. -/
 theorem coe_decompose_mul_of_right_mem_of_le (b_mem : b ∈ 𝒜 i) (h : i ≤ n) :
     (decompose 𝒜 (a * b) n : A) = decompose 𝒜 a (n - i) * b :=
@@ -459,10 +405,7 @@ theorem coe_decompose_mul_of_right_mem_of_le (b_mem : b ∈ 𝒜 i) (h : i ≤ n
 #align direct_sum.coe_decompose_mul_of_right_mem_of_le DirectSum.coe_decompose_mul_of_right_mem_of_le
 
 /- warning: direct_sum.coe_decompose_mul_of_left_mem -> DirectSum.coe_decompose_mul_of_left_mem is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : Semiring.{u2} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u3, u2} σ A] [_inst_5 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {i : ι} [_inst_7 : Sub.{u1} ι] [_inst_8 : OrderedSub.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))) _inst_7] [_inst_9 : ContravariantClass.{u1, u1} ι ι (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))))) (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))))] (n : ι) [_inst_10 : Decidable (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n)], (Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) a (𝒜 i)) -> (Eq.{succ u2} A ((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 A _inst_4) (𝒜 n)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 n)))))) (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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) a b)) n)) (ite.{succ u2} A (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n) _inst_10 (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) a ((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 A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n 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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) b) (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i)))) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1)))))))))
-but is expected to have type
-  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : Semiring.{u2} A] [_inst_2 : DecidableEq.{succ u3} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u3} ι] [_inst_4 : SetLike.{u1, u2} σ A] [_inst_5 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {i : ι} [_inst_7 : Sub.{u3} ι] [_inst_8 : OrderedSub.{u3} ι (Preorder.toLE.{u3} ι (PartialOrder.toPreorder.{u3} ι (OrderedAddCommMonoid.toPartialOrder.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))) (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3))))) _inst_7] [_inst_9 : ContravariantClass.{u3, u3} ι ι (fun (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3356 : ι) (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3358 : ι) => HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))))) x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3356 x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3358) (fun (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3371 : ι) (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3373 : ι) => LE.le.{u3} ι (Preorder.toLE.{u3} ι (PartialOrder.toPreorder.{u3} ι (OrderedAddCommMonoid.toPartialOrder.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))) x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3371 x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3373)] (n : ι) [_inst_10 : Decidable (LE.le.{u3} ι (Preorder.toLE.{u3} ι (PartialOrder.toPreorder.{u3} ι (OrderedAddCommMonoid.toPartialOrder.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))) i n)], (Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) a (𝒜 i)) -> (Eq.{succ u2} A (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_4 (𝒜 n))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1)))) a b)) n)) (ite.{succ u2} A (LE.le.{u3} ι (Preorder.toLE.{u3} ι (PartialOrder.toPreorder.{u3} ι (OrderedAddCommMonoid.toPartialOrder.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))) i n) _inst_10 (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1)))) a (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_4 (𝒜 (HSub.hSub.{u3, u3, u3} ι ι ι (instHSub.{u3} ι _inst_7) n i)))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) b) (HSub.hSub.{u3, u3, u3} ι ι ι (instHSub.{u3} ι _inst_7) n i)))) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_1))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_left_mem DirectSum.coe_decompose_mul_of_left_memₓ'. -/
 theorem coe_decompose_mul_of_left_mem (n) [Decidable (i ≤ n)] (a_mem : a ∈ 𝒜 i) :
     (decompose 𝒜 (a * b) n : A) = if i ≤ n then a * decompose 𝒜 b (n - i) else 0 :=
@@ -472,10 +415,7 @@ theorem coe_decompose_mul_of_left_mem (n) [Decidable (i ≤ n)] (a_mem : a ∈ 
 #align direct_sum.coe_decompose_mul_of_left_mem DirectSum.coe_decompose_mul_of_left_mem
 
 /- warning: direct_sum.coe_decompose_mul_of_right_mem -> DirectSum.coe_decompose_mul_of_right_mem is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : Semiring.{u2} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u3, u2} σ A] [_inst_5 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {i : ι} [_inst_7 : Sub.{u1} ι] [_inst_8 : OrderedSub.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))) _inst_7] [_inst_9 : ContravariantClass.{u1, u1} ι ι (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))))) (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))))] (n : ι) [_inst_10 : Decidable (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n)], (Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) b (𝒜 i)) -> (Eq.{succ u2} A ((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 A _inst_4) (𝒜 n)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 n)))))) (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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) a b)) n)) (ite.{succ u2} A (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n) _inst_10 (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) ((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 A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n 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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) a) (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) b) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1)))))))))
-but is expected to have type
-  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : Semiring.{u2} A] [_inst_2 : DecidableEq.{succ u3} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u3} ι] [_inst_4 : SetLike.{u1, u2} σ A] [_inst_5 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {i : ι} [_inst_7 : Sub.{u3} ι] [_inst_8 : OrderedSub.{u3} ι (Preorder.toLE.{u3} ι (PartialOrder.toPreorder.{u3} ι (OrderedAddCommMonoid.toPartialOrder.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))) (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3))))) _inst_7] [_inst_9 : ContravariantClass.{u3, u3} ι ι (fun (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3542 : ι) (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3544 : ι) => HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))))) x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3542 x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3544) (fun (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3557 : ι) (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3559 : ι) => LE.le.{u3} ι (Preorder.toLE.{u3} ι (PartialOrder.toPreorder.{u3} ι (OrderedAddCommMonoid.toPartialOrder.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))) x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3557 x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3559)] (n : ι) [_inst_10 : Decidable (LE.le.{u3} ι (Preorder.toLE.{u3} ι (PartialOrder.toPreorder.{u3} ι (OrderedAddCommMonoid.toPartialOrder.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))) i n)], (Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) b (𝒜 i)) -> (Eq.{succ u2} A (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_4 (𝒜 n))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1)))) a b)) n)) (ite.{succ u2} A (LE.le.{u3} ι (Preorder.toLE.{u3} ι (PartialOrder.toPreorder.{u3} ι (OrderedAddCommMonoid.toPartialOrder.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))) i n) _inst_10 (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1)))) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_4 (𝒜 (HSub.hSub.{u3, u3, u3} ι ι ι (instHSub.{u3} ι _inst_7) n i)))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) a) (HSub.hSub.{u3, u3, u3} ι ι ι (instHSub.{u3} ι _inst_7) n i))) b) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_1))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_right_mem DirectSum.coe_decompose_mul_of_right_memₓ'. -/
 theorem coe_decompose_mul_of_right_mem (n) [Decidable (i ≤ n)] (b_mem : b ∈ 𝒜 i) :
     (decompose 𝒜 (a * b) n : A) = if i ≤ n then decompose 𝒜 a (n - i) * b else 0 :=

1b0a28e1

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -319,7 +319,7 @@ def GradedAlgebra.proj (𝒜 : ι → Submodule R A) [GradedAlgebra 𝒜] (i : 
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_3 : CommSemiring.{u2} R] [_inst_4 : Semiring.{u3} A] [_inst_5 : Algebra.{u2, u3} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] (i : ι) (r : A), Eq.{succ u3} A (coeFn.{succ u3, succ u3} (LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (_x : LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) => A -> A) (LinearMap.hasCoeToFun.{u2, u2, u3, u3} R R A A (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3)))) (GradedAlgebra.proj.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 i) r) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) A (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) A (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) A (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) A (coeSubtype.{succ u3} A (fun (x : A) => Membership.Mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i)))))) (coeFn.{succ (max u1 u3), max (succ u1) (succ u3)} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (fun (_x : DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (coeFn.{max 1 (max (succ u3) (succ (max u1 u3))) (succ (max u1 u3)) (succ u3), max (succ u3) (succ (max u1 u3))} (Equiv.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (fun (_x : Equiv.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) => A -> (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (Equiv.hasCoeToFun.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (DirectSum.decompose.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6)) r) i))
 but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_3 : CommSemiring.{u2} R] [_inst_4 : Semiring.{u3} A] [_inst_5 : Algebra.{u2, u3} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] (i : ι) (r : A), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) r) (FunLike.coe.{succ u3, succ u3, succ u3} (LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u3} R R A A (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3)))) (GradedAlgebra.proj.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 i) r) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 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} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 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)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (DirectSum.decompose.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6)) r) i))
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_3 : CommSemiring.{u2} R] [_inst_4 : Semiring.{u3} A] [_inst_5 : Algebra.{u2, u3} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] (i : ι) (r : A), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) r) (FunLike.coe.{succ u3, succ u3, succ u3} (LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u3} R R A A (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3)))) (GradedAlgebra.proj.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 i) r) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 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} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 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)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (DirectSum.decompose.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6)) r) i))
 Case conversion may be inaccurate. Consider using '#align graded_algebra.proj_apply GradedAlgebra.proj_applyₓ'. -/
 @[simp]
 theorem GradedAlgebra.proj_apply (i : ι) (r : A) :
@@ -331,7 +331,7 @@ theorem GradedAlgebra.proj_apply (i : ι) (r : A) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_3 : CommSemiring.{u2} R] [_inst_4 : Semiring.{u3} A] [_inst_5 : Algebra.{u2, u3} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] (a : DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u3} ι (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (i : ι), Eq.{succ u3} A (coeFn.{succ u3, succ u3} (LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (_x : LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) => A -> A) (LinearMap.hasCoeToFun.{u2, u2, u3, u3} R R A A (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3)))) (GradedAlgebra.proj.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 i) (coeFn.{max 1 (max (succ (max u1 u3)) (succ u3)) (succ u3) (succ (max u1 u3)), max (succ (max u1 u3)) (succ u3)} (Equiv.{succ (max u1 u3), succ u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (fun (_x : Equiv.{succ (max u1 u3), succ u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) => (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) -> A) (Equiv.hasCoeToFun.{succ (max u1 u3), succ u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (Equiv.symm.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.decompose.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6))) a)) (coeFn.{max 1 (max (succ (max u1 u3)) (succ u3)) (succ u3) (succ (max u1 u3)), max (succ (max u1 u3)) (succ u3)} (Equiv.{succ (max u1 u3), succ u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (fun (_x : Equiv.{succ (max u1 u3), succ u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) => (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) -> A) (Equiv.hasCoeToFun.{succ (max u1 u3), succ u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (Equiv.symm.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.decompose.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6))) (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ u3) (succ (max u1 u3))} (AddMonoidHom.{u3, max u1 u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (AddMonoid.toAddZeroClass.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (AddCommMonoid.toAddMonoid.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.addCommMonoid.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))))) (fun (_x : AddMonoidHom.{u3, max u1 u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (AddMonoid.toAddZeroClass.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (AddCommMonoid.toAddMonoid.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.addCommMonoid.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))))) => (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) -> (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (AddMonoidHom.hasCoeToFun.{u3, max u1 u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (AddMonoid.toAddZeroClass.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (AddCommMonoid.toAddMonoid.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.addCommMonoid.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))))) (DirectSum.of.{u1, u3} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i) (coeFn.{succ (max u1 u3), max (succ u1) (succ u3)} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u3} ι (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (fun (_x : DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u3} ι (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) => forall (i : ι), coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u3} ι (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) a i)))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddMonoid.{u3} ι] [_inst_3 : CommSemiring.{u1} R] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u3, u1, u2} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] (a : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) (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} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (fun (a : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => A) a) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.decompose.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6))) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_3) (CommSemiring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R A A (CommSemiring.toSemiring.{u1} R _inst_3) (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3)))) (GradedAlgebra.proj.{u3, u1, u2} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 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} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (fun (_x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.decompose.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6))) a)) (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} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (fun (_x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.decompose.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (AddMonoidHom.{u2, max u2 u3} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))) ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (_x : (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) => DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) _x) (AddHomClass.toFunLike.{max u3 u2, u2, max u3 u2} (AddMonoidHom.{u2, max u2 u3} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))) ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddZeroClass.toAdd.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)))) (AddZeroClass.toAdd.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))) (AddMonoidHomClass.toAddHomClass.{max u3 u2, u2, max u3 u2} (AddMonoidHom.{u2, max u2 u3} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))) ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)))) (AddMonoidHom.addMonoidHomClass.{u2, max u3 u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))))) (DirectSum.of.{u3, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i) i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i) i))) i)) a i)))
+  forall {ι : Type.{u3}} {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddMonoid.{u3} ι] [_inst_3 : CommSemiring.{u1} R] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u3, u1, u2} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] (a : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) (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} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (fun (a : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => A) a) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.decompose.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6))) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_3) (CommSemiring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R A A (CommSemiring.toSemiring.{u1} R _inst_3) (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3)))) (GradedAlgebra.proj.{u3, u1, u2} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 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} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (fun (_x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.decompose.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6))) a)) (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} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (fun (_x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.decompose.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (AddMonoidHom.{u2, max u2 u3} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))) ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (_x : (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) => DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) _x) (AddHomClass.toFunLike.{max u3 u2, u2, max u3 u2} (AddMonoidHom.{u2, max u2 u3} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))) ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddZeroClass.toAdd.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)))) (AddZeroClass.toAdd.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))) (AddMonoidHomClass.toAddHomClass.{max u3 u2, u2, max u3 u2} (AddMonoidHom.{u2, max u2 u3} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))) ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)))) (AddMonoidHom.addMonoidHomClass.{u2, max u3 u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))))) (DirectSum.of.{u3, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i) i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i) i))) i)) a i)))
 Case conversion may be inaccurate. Consider using '#align graded_algebra.proj_recompose GradedAlgebra.proj_recomposeₓ'. -/
 theorem GradedAlgebra.proj_recompose (a : ⨁ i, 𝒜 i) (i : ι) :
     GradedAlgebra.proj 𝒜 i ((decompose 𝒜).symm a) = (decompose 𝒜).symm (of _ i (a i)) := by
@@ -342,7 +342,7 @@ theorem GradedAlgebra.proj_recompose (a : ⨁ i, 𝒜 i) (i : ι) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_3 : CommSemiring.{u2} R] [_inst_4 : Semiring.{u3} A] [_inst_5 : Algebra.{u2, u3} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] [_inst_7 : DecidableEq.{succ u3} A] (r : A) (i : ι), Iff (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i (Dfinsupp.support.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i)))) (fun (i : ι) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) => Ne.decidable.{succ u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (fun (a : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (b : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) => Subtype.decidableEq.{u3} A (fun (x : A) => Membership.Mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i)) (fun (a : A) (b : A) => _inst_7 a b) a b) x (OfNat.ofNat.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) 0 (OfNat.mk.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) 0 (Zero.zero.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (AddZeroClass.toHasZero.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i)))))))) (coeFn.{max 1 (max (succ u3) (succ (max u1 u3))) (succ (max u1 u3)) (succ u3), max (succ u3) (succ (max u1 u3))} (Equiv.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (fun (_x : Equiv.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) => A -> (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (Equiv.hasCoeToFun.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (DirectSum.decompose.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6)) r))) (Ne.{succ u3} A (coeFn.{succ u3, succ u3} (LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (_x : LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) => A -> A) (LinearMap.hasCoeToFun.{u2, u2, u3, u3} R R A A (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3)))) (GradedAlgebra.proj.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 i) r) (OfNat.ofNat.{u3} A 0 (OfNat.mk.{u3} A 0 (Zero.zero.{u3} A (MulZeroClass.toHasZero.{u3} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))))))
 but is expected to have type
-  forall {ι : Type.{u2}} {R : Type.{u1}} {A : Type.{u3}} [_inst_1 : DecidableEq.{succ u2} ι] [_inst_2 : AddMonoid.{u2} ι] [_inst_3 : CommSemiring.{u1} R] [_inst_4 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u3} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u2, u1, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] [_inst_7 : DecidableEq.{succ u3} A] (r : A) (i : ι), Iff (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i (Dfinsupp.support.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 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} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i))) (fun (i : ι) (x : Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) => instDecidableNot (Eq.{succ u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) x (OfNat.ofNat.{u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) 0 (Zero.toOfNat0.{u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i)))))) (Subtype.instDecidableEqSubtype.{u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i)) (fun (a : A) (b : A) => _inst_7 a b) x (OfNat.ofNat.{u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) 0 (Zero.toOfNat0.{u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i))))))) (FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (Equiv.{succ u3, max (succ u3) (succ u2)} A (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u2) (succ u3)} A (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (DirectSum.decompose.{u2, u3, u3} ι A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u2, u3, u3} ι A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6)) r))) (Ne.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) r) (FunLike.coe.{succ u3, succ u3, succ u3} (LinearMap.{u1, u1, u3, u3} R R (CommSemiring.toSemiring.{u1} R _inst_3) (CommSemiring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u3} R R A A (CommSemiring.toSemiring.{u1} R _inst_3) (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3)))) (GradedAlgebra.proj.{u2, u1, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 i) r) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) r) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) r) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) r) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) r) _inst_4)))))
+  forall {ι : Type.{u2}} {R : Type.{u1}} {A : Type.{u3}} [_inst_1 : DecidableEq.{succ u2} ι] [_inst_2 : AddMonoid.{u2} ι] [_inst_3 : CommSemiring.{u1} R] [_inst_4 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u3} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u2, u1, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] [_inst_7 : DecidableEq.{succ u3} A] (r : A) (i : ι), Iff (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i (Dfinsupp.support.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 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} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i))) (fun (i : ι) (x : Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) => instDecidableNot (Eq.{succ u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) x (OfNat.ofNat.{u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) 0 (Zero.toOfNat0.{u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i)))))) (Subtype.instDecidableEqSubtype.{u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i)) (fun (a : A) (b : A) => _inst_7 a b) x (OfNat.ofNat.{u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) 0 (Zero.toOfNat0.{u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i))))))) (FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (Equiv.{succ u3, max (succ u3) (succ u2)} A (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u2) (succ u3)} A (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (DirectSum.decompose.{u2, u3, u3} ι A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u2, u3, u3} ι A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6)) r))) (Ne.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) r) (FunLike.coe.{succ u3, succ u3, succ u3} (LinearMap.{u1, u1, u3, u3} R R (CommSemiring.toSemiring.{u1} R _inst_3) (CommSemiring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u3} R R A A (CommSemiring.toSemiring.{u1} R _inst_3) (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3)))) (GradedAlgebra.proj.{u2, u1, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 i) r) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) r) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) r) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) r) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : A) => A) r) _inst_4)))))
 Case conversion may be inaccurate. Consider using '#align graded_algebra.mem_support_iff GradedAlgebra.mem_support_iffₓ'. -/
 theorem GradedAlgebra.mem_support_iff [DecidableEq A] (r : A) (i : ι) :
     i ∈ (decompose 𝒜 r).support ↔ GradedAlgebra.proj 𝒜 i r ≠ 0 :=

1b0a28e1

bump to nightly-2023-05-22-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/1b0a28e1c93409dbf6d69526863cd9984ef652ce

5dfda1a5

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Kevin Buzzard, Jujian Zhang
 
 ! This file was ported from Lean 3 source module ring_theory.graded_algebra.basic
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 1b0a28e1c93409dbf6d69526863cd9984ef652ce
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Algebra.DirectSum.Ring
 /-!
 # Internally-graded rings and algebras
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines the typeclass `graded_algebra 𝒜`, for working with an algebra `A` that is
 internally graded by a collection of submodules `𝒜 : ι → submodule R A`.
 See the docstring of that typeclass for more information.

70fd9563

bump to nightly-2023-05-20-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/f51de8769c34652d82d1c8e5f8f18f8374782bed

96840968

Diff

@@ -58,6 +58,7 @@ include A
 
 open DirectSum
 
+#print GradedRing /-
 /-- An internally-graded `R`-algebra `A` is one that can be decomposed into a collection
 of `submodule R A`s indexed by `ι` such that the canonical map `A → ⨁ i, 𝒜 i` is bijective and
 respects multiplication, i.e. the product of an element of degree `i` and an element of degree `j`
@@ -69,11 +70,18 @@ algebra structure `direct_sum.galgebra R (λ i, ↥(𝒜 i))`, which in turn mak
 -/
 class GradedRing (𝒜 : ι → σ) extends SetLike.GradedMonoid 𝒜, DirectSum.Decomposition 𝒜
 #align graded_ring GradedRing
+-/
 
 variable [GradedRing 𝒜]
 
 namespace DirectSum
 
+/- warning: direct_sum.decompose_ring_equiv -> DirectSum.decomposeRingEquiv is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u3, u2} σ A] [_inst_7 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜], RingEquiv.{u2, max u1 u2} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))) (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))) (Distrib.toHasMul.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.nonUnitalNonAssocSemiring.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i) (SetLike.gnonUnitalNonAssocSemiring.{u1, u3, u2} ι σ A (fun (a : ι) (b : ι) => _inst_1 a b) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)) _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) (DirectSum.decomposeRingEquiv._proof_1.{u1, u2, u3} ι A σ _inst_1 _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))))) (Distrib.toHasAdd.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.nonUnitalNonAssocSemiring.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i) (SetLike.gnonUnitalNonAssocSemiring.{u1, u3, u2} ι σ A (fun (a : ι) (b : ι) => _inst_1 a b) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)) _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) (DirectSum.decomposeRingEquiv._proof_1.{u1, u2, u3} ι A σ _inst_1 _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)))))
+but is expected to have type
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u3, u2} σ A] [_inst_7 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜], RingEquiv.{u2, max u2 u1} A (DirectSum.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u3} A σ (SetLike.instMembership.{u3, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u3} A σ (SetLike.instMembership.{u3, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.instNonUnitalNonAssocSemiringDirectSum.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u3} A σ (SetLike.instMembership.{u3, u2} σ A _inst_6) x (𝒜 i))) (AddZeroClass.toAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i) (SetLike.gnonUnitalNonAssocSemiring.{u1, u3, u2} ι σ A (AddZeroClass.toAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)) _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedMul.{u1, u2, u3} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8))))) (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))) (Distrib.toAdd.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u3} A σ (SetLike.instMembership.{u3, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u3} A σ (SetLike.instMembership.{u3, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.instNonUnitalNonAssocSemiringDirectSum.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u3} A σ (SetLike.instMembership.{u3, u2} σ A _inst_6) x (𝒜 i))) (AddZeroClass.toAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i) (SetLike.gnonUnitalNonAssocSemiring.{u1, u3, u2} ι σ A (AddZeroClass.toAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)) _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedMul.{u1, u2, u3} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8))))))
+Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_ring_equiv DirectSum.decomposeRingEquivₓ'. -/
 /-- If `A` is graded by `ι` with degree `i` component `𝒜 i`, then it is isomorphic as
 a ring to a direct sum of components. -/
 def decomposeRingEquiv : A ≃+* ⨁ i, 𝒜 i :=
@@ -84,21 +92,45 @@ def decomposeRingEquiv : A ≃+* ⨁ i, 𝒜 i :=
       map_add' := (coeRingHom 𝒜).map_add }
 #align direct_sum.decompose_ring_equiv DirectSum.decomposeRingEquiv
 
+/- warning: direct_sum.decompose_one -> DirectSum.decompose_one is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u3, u2} σ A] [_inst_7 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜], 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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))))) (OfNat.ofNat.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) 1 (OfNat.mk.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) 1 (One.one.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.hasOne.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddZeroClass.toHasZero.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (SetLike.gOne.{u1, u2, u3} ι A σ _inst_6 (MulOneClass.toHasOne.{u2} A (Monoid.toMulOneClass.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)))) (AddZeroClass.toHasZero.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.to_gradedOne.{u1, u2, u3} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.to_gradedMonoid.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))))))
+but is expected to have type
+  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddMonoid.{u3} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u1, u2} σ A] [_inst_7 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜], Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_4)))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_4)))) (OfNat.ofNat.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_4)))) 1 (One.toOfNat1.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_4)))) (DirectSum.instOneDirectSum.{u3, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (AddMonoid.toZero.{u3} ι _inst_2) (SetLike.gOne.{u3, u2, u1} ι A σ _inst_6 (Semiring.toOne.{u2} A _inst_4) (AddMonoid.toZero.{u3} ι _inst_2) (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedOne.{u3, u2, u1} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))))
+Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_one DirectSum.decompose_oneₓ'. -/
 @[simp]
 theorem decompose_one : decompose 𝒜 (1 : A) = 1 :=
   map_one (decomposeRingEquiv 𝒜)
 #align direct_sum.decompose_one DirectSum.decompose_one
 
+/- warning: direct_sum.decompose_symm_one -> DirectSum.decompose_symm_one is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u3, u2} σ A] [_inst_7 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜], Eq.{succ u2} A (coeFn.{max 1 (max (succ (max u1 u2)) (succ u2)) (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) => (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) -> A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) (OfNat.ofNat.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) 1 (OfNat.mk.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) 1 (One.one.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.hasOne.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddZeroClass.toHasZero.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (SetLike.gOne.{u1, u2, u3} ι A σ _inst_6 (MulOneClass.toHasOne.{u2} A (Monoid.toMulOneClass.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)))) (AddZeroClass.toHasZero.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.to_gradedOne.{u1, u2, u3} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.to_gradedMonoid.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))))))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))))
+but is expected to have type
+  forall {ι : Type.{u2}} {A : Type.{u3}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} ι] [_inst_2 : AddMonoid.{u2} ι] [_inst_4 : Semiring.{u3} A] [_inst_6 : SetLike.{u1, u3} σ A] [_inst_7 : AddSubmonoidClass.{u1, u3} σ A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u2, u3, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜], Eq.{succ u3} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) (OfNat.ofNat.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) 1 (One.toOfNat1.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.instOneDirectSum.{u2, u3} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (AddMonoid.toZero.{u2} ι _inst_2) (SetLike.gOne.{u2, u3, u1} ι A σ _inst_6 (Semiring.toOne.{u3} A _inst_4) (AddMonoid.toZero.{u2} ι _inst_2) (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedOne.{u2, u3, u1} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u2, u3, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 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} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (fun (_x : DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u3), succ u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u3, max (succ u2) (succ u3)} A (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u2, u3, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u2, u3, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) (OfNat.ofNat.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) 1 (One.toOfNat1.{max u2 u3} (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.instOneDirectSum.{u2, u3} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (AddMonoid.toZero.{u2} ι _inst_2) (SetLike.gOne.{u2, u3, u1} ι A σ _inst_6 (Semiring.toOne.{u3} A _inst_4) (AddMonoid.toZero.{u2} ι _inst_2) (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedOne.{u2, u3, u1} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u2, u3, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))))) (OfNat.ofNat.{u3} A 1 (One.toOfNat1.{u3} A (Semiring.toOne.{u3} A _inst_4)))
+Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_one DirectSum.decompose_symm_oneₓ'. -/
 @[simp]
 theorem decompose_symm_one : (decompose 𝒜).symm 1 = (1 : A) :=
   map_one (decomposeRingEquiv 𝒜).symm
 #align direct_sum.decompose_symm_one DirectSum.decompose_symm_one
 
+/- warning: direct_sum.decompose_mul -> DirectSum.decompose_mul is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u3, u2} σ A] [_inst_7 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] (x : A) (y : A), 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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) x y)) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (instHMul.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (Distrib.toHasMul.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.nonUnitalNonAssocSemiring.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)) (SetLike.gnonUnitalNonAssocSemiring.{u1, u3, u2} ι σ A (fun (a : ι) (b : ι) => _inst_1 a b) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)) _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.to_gradedMul.{u1, u2, u3} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.to_gradedMonoid.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8))))))) (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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) x) (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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) y))
+but is expected to have type
+  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddMonoid.{u3} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u1, u2} σ A] [_inst_7 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] (x : A) (y : A), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))) x y)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))) x y)) (HMul.hMul.{max u3 u2, max u3 u2, max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) x) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) y) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) x) (instHMul.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) x) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) x) (DirectSum.instNonUnitalNonAssocSemiringDirectSum.{u3, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι _inst_2)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)) (SetLike.gnonUnitalNonAssocSemiring.{u3, u1, u2} ι σ A (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)) _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedMul.{u3, u2, u1} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8)))))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) x) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) y))
+Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_mul DirectSum.decompose_mulₓ'. -/
 @[simp]
 theorem decompose_mul (x y : A) : decompose 𝒜 (x * y) = decompose 𝒜 x * decompose 𝒜 y :=
   map_mul (decomposeRingEquiv 𝒜) x y
 #align direct_sum.decompose_mul DirectSum.decompose_mul
 
+/- warning: direct_sum.decompose_symm_mul -> DirectSum.decompose_symm_mul is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u3, u2} σ A] [_inst_7 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] (x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (y : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)), Eq.{succ u2} A (coeFn.{max 1 (max (succ (max u1 u2)) (succ u2)) (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) => (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) -> A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (instHMul.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (Distrib.toHasMul.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (NonUnitalNonAssocSemiring.toDistrib.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.nonUnitalNonAssocSemiring.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)) (SetLike.gnonUnitalNonAssocSemiring.{u1, u3, u2} ι σ A (fun (a : ι) (b : ι) => _inst_1 a b) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)) _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.to_gradedMul.{u1, u2, u3} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.to_gradedMonoid.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8))))))) x y)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (coeFn.{max 1 (max (succ (max u1 u2)) (succ u2)) (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) => (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) -> A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) x) (coeFn.{max 1 (max (succ (max u1 u2)) (succ u2)) (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) => (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) -> A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) y))
+but is expected to have type
+  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddMonoid.{u3} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u1, u2} σ A] [_inst_7 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] (x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (y : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) (HMul.hMul.{max u3 u2, max u3 u2, max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (instHMul.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.instNonUnitalNonAssocSemiringDirectSum.{u3, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι _inst_2)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i) (SetLike.gnonUnitalNonAssocSemiring.{u3, u1, u2} ι σ A (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)) _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedMul.{u3, u2, u1} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8)))))) x y)) (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} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (fun (_x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) (HMul.hMul.{max u3 u2, max u3 u2, max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (instHMul.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (NonUnitalNonAssocSemiring.toMul.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (DirectSum.instNonUnitalNonAssocSemiringDirectSum.{u3, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι _inst_2)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i) (SetLike.gnonUnitalNonAssocSemiring.{u3, u1, u2} ι σ A (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)) _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedMul.{u3, u2, u1} ι A σ _inst_6 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_4)) _inst_2 (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 (fun (i : ι) => 𝒜 i) _inst_8)))))) x y)) (HMul.hMul.{u2, u2, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) x) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) y) ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) x) (instHMul.{u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) x) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) x) _inst_4)))) (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} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (fun (_x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) x) (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} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (fun (_x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) y))
+Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_symm_mul DirectSum.decompose_symm_mulₓ'. -/
 @[simp]
 theorem decompose_symm_mul (x y : ⨁ i, 𝒜 i) :
     (decompose 𝒜).symm (x * y) = (decompose 𝒜).symm x * (decompose 𝒜).symm y :=
@@ -107,24 +139,44 @@ theorem decompose_symm_mul (x y : ⨁ i, 𝒜 i) :
 
 end DirectSum
 
+#print GradedRing.proj /-
 /-- The projection maps of a graded ring -/
 def GradedRing.proj (i : ι) : A →+ A :=
   (AddSubmonoidClass.Subtype (𝒜 i)).comp <|
     (Dfinsupp.evalAddMonoidHom i).comp <|
       RingHom.toAddMonoidHom <| RingEquiv.toRingHom <| DirectSum.decomposeRingEquiv 𝒜
 #align graded_ring.proj GradedRing.proj
+-/
 
+/- warning: graded_ring.proj_apply -> GradedRing.proj_apply is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u3, u2} σ A] [_inst_7 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] (i : ι) (r : A), Eq.{succ u2} A (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (fun (_x : AddMonoidHom.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) => A -> A) (AddMonoidHom.hasCoeToFun.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (GradedRing.proj.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8 i) r) ((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 A _inst_6) (𝒜 i)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_6) x (𝒜 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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) r) i))
+but is expected to have type
+  forall {ι : Type.{u2}} {A : Type.{u3}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} ι] [_inst_2 : AddMonoid.{u2} ι] [_inst_4 : Semiring.{u3} A] [_inst_6 : SetLike.{u1, u3} σ A] [_inst_7 : AddSubmonoidClass.{u1, u3} σ A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u2, u3, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] (i : ι) (r : A), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) r) (FunLike.coe.{succ u3, succ u3, succ u3} (AddMonoidHom.{u3, u3} A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) _x) (AddHomClass.toFunLike.{u3, u3, u3} (AddMonoidHom.{u3, u3} A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) A A (AddZeroClass.toAdd.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) (AddZeroClass.toAdd.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) (AddMonoidHomClass.toAddHomClass.{u3, u3, u3} (AddMonoidHom.{u3, u3} A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoidHom.addMonoidHomClass.{u3, u3} A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))))) (GradedRing.proj.{u2, u3, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8 i) r) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u1, u3} σ A _inst_6 (𝒜 i))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Dfinsupp.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (Equiv.{succ u3, max (succ u3) (succ u2)} A (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u2) (succ u3)} A (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u1} A σ (SetLike.instMembership.{u1, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u2, u3, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u2, u3, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) r) i))
+Case conversion may be inaccurate. Consider using '#align graded_ring.proj_apply GradedRing.proj_applyₓ'. -/
 @[simp]
 theorem GradedRing.proj_apply (i : ι) (r : A) :
     GradedRing.proj 𝒜 i r = (decompose 𝒜 r : ⨁ i, 𝒜 i) i :=
   rfl
 #align graded_ring.proj_apply GradedRing.proj_apply
 
+/- warning: graded_ring.proj_recompose -> GradedRing.proj_recompose is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u3, u2} σ A] [_inst_7 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] (a : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (i : ι), Eq.{succ u2} A (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (fun (_x : AddMonoidHom.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) => A -> A) (AddMonoidHom.hasCoeToFun.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (GradedRing.proj.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8 i) (coeFn.{max 1 (max (succ (max u1 u2)) (succ u2)) (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) => (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) -> A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) a)) (coeFn.{max 1 (max (succ (max u1 u2)) (succ u2)) (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) => (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) -> A) (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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (AddMonoidHom.{u2, max u1 u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (AddMonoid.toAddZeroClass.{u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddCommMonoid.toAddMonoid.{u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (AddMonoid.toAddZeroClass.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (AddCommMonoid.toAddMonoid.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.addCommMonoid.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))))) (fun (_x : AddMonoidHom.{u2, max u1 u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (AddMonoid.toAddZeroClass.{u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddCommMonoid.toAddMonoid.{u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (AddMonoid.toAddZeroClass.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (AddCommMonoid.toAddMonoid.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.addCommMonoid.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))))) => (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (AddMonoidHom.hasCoeToFun.{u2, max u1 u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (AddMonoid.toAddZeroClass.{u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddCommMonoid.toAddMonoid.{u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (AddMonoid.toAddZeroClass.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (AddCommMonoid.toAddMonoid.{max u1 u2} (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.addCommMonoid.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))))) (DirectSum.of.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)) 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 A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) a i)))
+but is expected to have type
+  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddMonoid.{u3} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u1, u2} σ A] [_inst_7 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] (a : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) (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} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (fun (a : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) a) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (AddMonoidHom.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) _x) (AddHomClass.toFunLike.{u2, u2, u2} (AddMonoidHom.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) A A (AddZeroClass.toAdd.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (AddZeroClass.toAdd.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (AddMonoidHomClass.toAddHomClass.{u2, u2, u2} (AddMonoidHom.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoidHom.addMonoidHomClass.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))))) (GradedRing.proj.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8 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} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (fun (_x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) a)) (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} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (fun (_x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (AddMonoidHom.{u2, max u2 u3} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))))) ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (_x : (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) => DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) _x) (AddHomClass.toFunLike.{max u3 u2, u2, max u3 u2} (AddMonoidHom.{u2, max u2 u3} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))))) ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddZeroClass.toAdd.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)))) (AddZeroClass.toAdd.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))))) (AddMonoidHomClass.toAddHomClass.{max u3 u2, u2, max u3 u2} (AddMonoidHom.{u2, max u2 u3} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))))) ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)))) (AddMonoidHom.addMonoidHomClass.{u2, max u3 u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i))))))) (DirectSum.of.{u3, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i) i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) i) ((fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_6) x (𝒜 i))) i) i) ((fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u1, u2} ι σ A _inst_4 _inst_6 _inst_7 𝒜 i) i))) i)) a i)))
+Case conversion may be inaccurate. Consider using '#align graded_ring.proj_recompose GradedRing.proj_recomposeₓ'. -/
 theorem GradedRing.proj_recompose (a : ⨁ i, 𝒜 i) (i : ι) :
     GradedRing.proj 𝒜 i ((decompose 𝒜).symm a) = (decompose 𝒜).symm (DirectSum.of _ i (a i)) := by
   rw [GradedRing.proj_apply, decompose_symm_of, Equiv.apply_symm_apply]
 #align graded_ring.proj_recompose GradedRing.proj_recompose
 
+/- warning: graded_ring.mem_support_iff -> GradedRing.mem_support_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u2} A] [_inst_6 : SetLike.{u3, u2} σ A] [_inst_7 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] [_inst_9 : forall (i : ι) (x : coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)), Decidable (Ne.{succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) x (OfNat.ofNat.{u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) 0 (OfNat.mk.{u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) 0 (Zero.zero.{u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (ZeroMemClass.zero.{u3, u2} σ A _inst_6 (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (AddSubmonoidClass.to_zeroMemClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) _inst_6 _inst_7) (𝒜 i))))))] (r : A) (i : ι), Iff (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i (Dfinsupp.support.{u1, u2} ι (fun (i : ι) => (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) i) (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => AddZeroClass.toHasZero.{u2} ((fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) i) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)) i)))) (fun (i : ι) (x : coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) => _inst_9 i x) (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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_6) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) r))) (Ne.{succ u2} A (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (fun (_x : AddMonoidHom.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) => A -> A) (AddMonoidHom.hasCoeToFun.{u2, u2} A A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))) (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (GradedRing.proj.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8 i) r) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))))))))
+but is expected to have type
+  forall {ι : Type.{u1}} {A : Type.{u3}} {σ : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_4 : Semiring.{u3} A] [_inst_6 : SetLike.{u2, u3} σ A] [_inst_7 : AddSubmonoidClass.{u2, u3} σ A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) _inst_6] (𝒜 : ι -> σ) [_inst_8 : GradedRing.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜] [_inst_9 : forall (i : ι) (x : Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))), Decidable (Ne.{succ u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))) x (OfNat.ofNat.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))) 0 (Zero.toOfNat0.{u3} (Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))) (ZeroMemClass.zero.{u2, u3} σ A _inst_6 (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_4)) (AddSubmonoidClass.toZeroMemClass.{u2, u3} σ A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) _inst_6 _inst_7) (𝒜 i)))))] (r : A) (i : ι), Iff (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i (Dfinsupp.support.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 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} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)) i))) (fun (i : ι) (x : Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))) => _inst_9 i x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, max (succ u1) (succ u3)} (Equiv.{succ u3, max (succ u3) (succ u1)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_6) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) σ _inst_6 _inst_7 (𝒜 i)))) (DirectSum.decompose.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) _inst_6 _inst_7 𝒜 (GradedRing.toDecomposition.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8)) r))) (Ne.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) r) (FunLike.coe.{succ u3, succ u3, succ u3} (AddMonoidHom.{u3, u3} A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) _x) (AddHomClass.toFunLike.{u3, u3, u3} (AddMonoidHom.{u3, u3} A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) A A (AddZeroClass.toAdd.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) (AddZeroClass.toAdd.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) (AddMonoidHomClass.toAddHomClass.{u3, u3, u3} (AddMonoidHom.{u3, u3} A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))) A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoidHom.addMonoidHomClass.{u3, u3} A A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))) (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4)))))))) (GradedRing.proj.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 _inst_6 _inst_7 𝒜 _inst_8 i) r) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) r) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) r) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) r) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : A) => A) r) _inst_4)))))
+Case conversion may be inaccurate. Consider using '#align graded_ring.mem_support_iff GradedRing.mem_support_iffₓ'. -/
 theorem GradedRing.mem_support_iff [∀ (i) (x : 𝒜 i), Decidable (x ≠ 0)] (r : A) (i : ι) :
     i ∈ (decompose 𝒜 r).support ↔ GradedRing.proj 𝒜 i r ≠ 0 :=
   Dfinsupp.mem_support_iff.trans ZeroMemClass.coe_eq_zero.Not.symm
@@ -142,6 +194,12 @@ variable {i j : ι}
 
 namespace DirectSum
 
+/- warning: direct_sum.coe_decompose_mul_add_of_left_mem -> DirectSum.coe_decompose_mul_add_of_left_mem is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : Semiring.{u2} A] [_inst_3 : SetLike.{u3, u2} σ A] [_inst_4 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) _inst_3] (𝒜 : ι -> σ) {i : ι} {j : ι} [_inst_5 : AddLeftCancelMonoid.{u1} ι] [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜] {a : A} {b : A}, (Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_3) a (𝒜 i)) -> (Eq.{succ u2} A ((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 A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_3) x (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))))))) (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 A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) a b)) (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) a ((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 A _inst_3) (𝒜 j)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 j)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 j)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 j)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_3) x (𝒜 j)))))) (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 A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) b) j))))
+but is expected to have type
+  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} A] [_inst_3 : SetLike.{u1, u2} σ A] [_inst_4 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) _inst_3] (𝒜 : ι -> σ) {i : ι} {j : ι} [_inst_5 : AddLeftCancelMonoid.{u3} ι] [_inst_6 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜] {a : A} {b : A}, (Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) a (𝒜 i)) -> (Eq.{succ u2} A (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_3 (𝒜 (HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5)))) i j)))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a b)) (HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5)))) i j))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_3 (𝒜 j))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) b) j))))
+Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_add_of_left_mem DirectSum.coe_decompose_mul_add_of_left_memₓ'. -/
 theorem coe_decompose_mul_add_of_left_mem [AddLeftCancelMonoid ι] [GradedRing 𝒜] {a b : A}
     (a_mem : a ∈ 𝒜 i) : (decompose 𝒜 (a * b) (i + j) : A) = a * decompose 𝒜 b j :=
   by
@@ -149,6 +207,12 @@ theorem coe_decompose_mul_add_of_left_mem [AddLeftCancelMonoid ι] [GradedRing 
   rw [decompose_mul, decompose_coe, coe_of_mul_apply_add]
 #align direct_sum.coe_decompose_mul_add_of_left_mem DirectSum.coe_decompose_mul_add_of_left_mem
 
+/- warning: direct_sum.coe_decompose_mul_add_of_right_mem -> DirectSum.coe_decompose_mul_add_of_right_mem is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : Semiring.{u2} A] [_inst_3 : SetLike.{u3, u2} σ A] [_inst_4 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) _inst_3] (𝒜 : ι -> σ) {i : ι} {j : ι} [_inst_5 : AddRightCancelMonoid.{u1} ι] [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜] {a : A} {b : A}, (Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_3) b (𝒜 j)) -> (Eq.{succ u2} A ((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 A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_3) x (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))))))) (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 A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) a b)) (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) ((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 A _inst_3) (𝒜 i)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_3) x (𝒜 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 A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) a) i)) b))
+but is expected to have type
+  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} A] [_inst_3 : SetLike.{u1, u2} σ A] [_inst_4 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) _inst_3] (𝒜 : ι -> σ) {i : ι} {j : ι} [_inst_5 : AddRightCancelMonoid.{u3} ι] [_inst_6 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜] {a : A} {b : A}, (Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) b (𝒜 j)) -> (Eq.{succ u2} A (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_3 (𝒜 (HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5)))) i j)))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a b)) (HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5)))) i j))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_3 (𝒜 i))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) a) i)) b))
+Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_add_of_right_mem DirectSum.coe_decompose_mul_add_of_right_memₓ'. -/
 theorem coe_decompose_mul_add_of_right_mem [AddRightCancelMonoid ι] [GradedRing 𝒜] {a b : A}
     (b_mem : b ∈ 𝒜 j) : (decompose 𝒜 (a * b) (i + j) : A) = decompose 𝒜 a i * b :=
   by
@@ -156,12 +220,24 @@ theorem coe_decompose_mul_add_of_right_mem [AddRightCancelMonoid ι] [GradedRing
   rw [decompose_mul, decompose_coe, coe_mul_of_apply_add]
 #align direct_sum.coe_decompose_mul_add_of_right_mem DirectSum.coe_decompose_mul_add_of_right_mem
 
+/- warning: direct_sum.decompose_mul_add_left -> DirectSum.decompose_mul_add_left is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : Semiring.{u2} A] [_inst_3 : SetLike.{u3, u2} σ A] [_inst_4 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) _inst_3] (𝒜 : ι -> σ) {i : ι} {j : ι} [_inst_5 : AddLeftCancelMonoid.{u1} ι] [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜] (a : coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) {b : A}, Eq.{succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) (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 A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) ((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 A _inst_3) (𝒜 i)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_3) x (𝒜 i)))))) a) b)) (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j)) (GradedMonoid.GMul.mul.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5))) (SetLike.gMul.{u1, u2, u3} ι A σ _inst_3 (MulOneClass.toHasMul.{u2} A (Monoid.toMulOneClass.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5))) (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.to_gradedMul.{u1, u2, u3} ι A σ _inst_3 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5) (fun (i : ι) => 𝒜 i) (GradedRing.to_gradedMonoid.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 (fun (i : ι) => 𝒜 i) _inst_6))) i j a (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 A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) b) j))
+but is expected to have type
+  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} A] [_inst_3 : SetLike.{u1, u2} σ A] [_inst_4 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) _inst_3] (𝒜 : ι -> σ) {i : ι} {j : ι} [_inst_5 : AddLeftCancelMonoid.{u3} ι] [_inst_6 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜] (a : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) {b : A}, Eq.{succ u2} ((fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5)))) i j)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_3 (𝒜 i))) a) b)) (HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5)))) i j)) (GradedMonoid.GMul.mul.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5))) (SetLike.gMul.{u3, u2, u1} ι A σ _inst_3 (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5))) (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedMul.{u3, u2, u1} ι A σ _inst_3 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5) (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 (fun (i : ι) => 𝒜 i) _inst_6))) i j a (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddLeftCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) b) j))
+Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_mul_add_left DirectSum.decompose_mul_add_leftₓ'. -/
 theorem decompose_mul_add_left [AddLeftCancelMonoid ι] [GradedRing 𝒜] (a : 𝒜 i) {b : A} :
     decompose 𝒜 (↑a * b) (i + j) =
       @GradedMonoid.GMul.mul ι (fun i => 𝒜 i) _ _ _ _ a (decompose 𝒜 b j) :=
   Subtype.ext <| coe_decompose_mul_add_of_left_mem 𝒜 a.2
 #align direct_sum.decompose_mul_add_left DirectSum.decompose_mul_add_left
 
+/- warning: direct_sum.decompose_mul_add_right -> DirectSum.decompose_mul_add_right is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : Semiring.{u2} A] [_inst_3 : SetLike.{u3, u2} σ A] [_inst_4 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) _inst_3] (𝒜 : ι -> σ) {i : ι} {j : ι} [_inst_5 : AddRightCancelMonoid.{u1} ι] [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜] {a : A} (b : coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 j)), Eq.{succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j))) (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 A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) a ((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 A _inst_3) (𝒜 j)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 j)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 j)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 j)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_3) x (𝒜 j)))))) b))) (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5)))) i j)) (GradedMonoid.GMul.mul.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5))) (SetLike.gMul.{u1, u2, u3} ι A σ _inst_3 (MulOneClass.toHasMul.{u2} A (Monoid.toMulOneClass.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5))) (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.to_gradedMul.{u1, u2, u3} ι A σ _inst_3 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5) (fun (i : ι) => 𝒜 i) (GradedRing.to_gradedMonoid.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 (fun (i : ι) => 𝒜 i) _inst_6))) i j (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 A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_3) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u1} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) a) i) b)
+but is expected to have type
+  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : Semiring.{u2} A] [_inst_3 : SetLike.{u1, u2} σ A] [_inst_4 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) _inst_3] (𝒜 : ι -> σ) {i : ι} {j : ι} [_inst_5 : AddRightCancelMonoid.{u3} ι] [_inst_6 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜] {a : A} (b : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 j))), Eq.{succ u2} ((fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5)))) i j)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) a (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_3 (𝒜 j))) b))) (HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5)))) i j)) (GradedMonoid.GMul.mul.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5))) (SetLike.gMul.{u3, u2, u1} ι A σ _inst_3 (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5))) (fun (i : ι) => 𝒜 i) (SetLike.GradedMonoid.toGradedMul.{u3, u2, u1} ι A σ _inst_3 (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5) (fun (i : ι) => 𝒜 i) (GradedRing.toGradedMonoid.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 (fun (i : ι) => 𝒜 i) _inst_6))) i j (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_3) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) σ _inst_3 _inst_4 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) _inst_3 _inst_4 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_1 a b) (AddRightCancelMonoid.toAddMonoid.{u3} ι _inst_5) _inst_2 _inst_3 _inst_4 𝒜 _inst_6)) a) i) b)
+Case conversion may be inaccurate. Consider using '#align direct_sum.decompose_mul_add_right DirectSum.decompose_mul_add_rightₓ'. -/
 theorem decompose_mul_add_right [AddRightCancelMonoid ι] [GradedRing 𝒜] {a : A} (b : 𝒜 j) :
     decompose 𝒜 (a * ↑b) (i + j) =
       @GradedMonoid.GMul.mul ι (fun i => 𝒜 i) _ _ _ _ (decompose 𝒜 a i) b :=
@@ -178,13 +254,16 @@ variable [DecidableEq ι] [AddMonoid ι] [CommSemiring R] [Semiring A] [Algebra
 
 variable (𝒜 : ι → Submodule R A)
 
+#print GradedAlgebra /-
 /-- A special case of `graded_ring` with `σ = submodule R A`. This is useful both because it
 can avoid typeclass search, and because it provides a more concise name. -/
 @[reducible]
 def GradedAlgebra :=
   GradedRing 𝒜
 #align graded_algebra GradedAlgebra
+-/
 
+#print GradedAlgebra.ofAlgHom /-
 /-- A helper to construct a `graded_algebra` when the `set_like.graded_monoid` structure is already
 available. This makes the `left_inv` condition easier to prove, and phrases the `right_inv`
 condition in a way that allows custom `@[ext]` lemmas to apply.
@@ -203,11 +282,13 @@ def GradedAlgebra.ofAlgHom [SetLike.GradedMonoid 𝒜] (decompose : A →ₐ[R]
     ext (i x) : 2
     exact (decompose.congr_arg <| DirectSum.coeAlgHom_of _ _ _).trans (left_inv i x)
 #align graded_algebra.of_alg_hom GradedAlgebra.ofAlgHom
+-/
 
 variable [GradedAlgebra 𝒜]
 
 namespace DirectSum
 
+#print DirectSum.decomposeAlgEquiv /-
 /-- If `A` is graded by `ι` with degree `i` component `𝒜 i`, then it is isomorphic as
 an algebra to a direct sum of components. -/
 @[simps]
@@ -218,27 +299,48 @@ def decomposeAlgEquiv : A ≃ₐ[R] ⨁ i, 𝒜 i :=
       map_add' := (coeAlgHom 𝒜).map_add
       commutes' := (coeAlgHom 𝒜).commutes }
 #align direct_sum.decompose_alg_equiv DirectSum.decomposeAlgEquiv
+-/
 
 end DirectSum
 
 open DirectSum
 
+#print GradedAlgebra.proj /-
 /-- The projection maps of graded algebra-/
 def GradedAlgebra.proj (𝒜 : ι → Submodule R A) [GradedAlgebra 𝒜] (i : ι) : A →ₗ[R] A :=
   (𝒜 i).Subtype.comp <| (Dfinsupp.lapply i).comp <| (decomposeAlgEquiv 𝒜).toAlgHom.toLinearMap
 #align graded_algebra.proj GradedAlgebra.proj
+-/
 
+/- warning: graded_algebra.proj_apply -> GradedAlgebra.proj_apply is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_3 : CommSemiring.{u2} R] [_inst_4 : Semiring.{u3} A] [_inst_5 : Algebra.{u2, u3} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] (i : ι) (r : A), Eq.{succ u3} A (coeFn.{succ u3, succ u3} (LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (_x : LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) => A -> A) (LinearMap.hasCoeToFun.{u2, u2, u3, u3} R R A A (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3)))) (GradedAlgebra.proj.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 i) r) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) A (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) A (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) A (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) A (coeSubtype.{succ u3} A (fun (x : A) => Membership.Mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i)))))) (coeFn.{succ (max u1 u3), max (succ u1) (succ u3)} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (fun (_x : DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (coeFn.{max 1 (max (succ u3) (succ (max u1 u3))) (succ (max u1 u3)) (succ u3), max (succ u3) (succ (max u1 u3))} (Equiv.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (fun (_x : Equiv.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) => A -> (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (Equiv.hasCoeToFun.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (DirectSum.decompose.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6)) r) i))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_3 : CommSemiring.{u2} R] [_inst_4 : Semiring.{u3} A] [_inst_5 : Algebra.{u2, u3} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] (i : ι) (r : A), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) r) (FunLike.coe.{succ u3, succ u3, succ u3} (LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u3, u3} R R A A (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3)))) (GradedAlgebra.proj.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 i) r) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 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} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 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)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (DirectSum.decompose.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6)) r) i))
+Case conversion may be inaccurate. Consider using '#align graded_algebra.proj_apply GradedAlgebra.proj_applyₓ'. -/
 @[simp]
 theorem GradedAlgebra.proj_apply (i : ι) (r : A) :
     GradedAlgebra.proj 𝒜 i r = (decompose 𝒜 r : ⨁ i, 𝒜 i) i :=
   rfl
 #align graded_algebra.proj_apply GradedAlgebra.proj_apply
 
+/- warning: graded_algebra.proj_recompose -> GradedAlgebra.proj_recompose is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_3 : CommSemiring.{u2} R] [_inst_4 : Semiring.{u3} A] [_inst_5 : Algebra.{u2, u3} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] (a : DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u3} ι (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (i : ι), Eq.{succ u3} A (coeFn.{succ u3, succ u3} (LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (_x : LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) => A -> A) (LinearMap.hasCoeToFun.{u2, u2, u3, u3} R R A A (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3)))) (GradedAlgebra.proj.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 i) (coeFn.{max 1 (max (succ (max u1 u3)) (succ u3)) (succ u3) (succ (max u1 u3)), max (succ (max u1 u3)) (succ u3)} (Equiv.{succ (max u1 u3), succ u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (fun (_x : Equiv.{succ (max u1 u3), succ u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) => (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) -> A) (Equiv.hasCoeToFun.{succ (max u1 u3), succ u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (Equiv.symm.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.decompose.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6))) a)) (coeFn.{max 1 (max (succ (max u1 u3)) (succ u3)) (succ u3) (succ (max u1 u3)), max (succ (max u1 u3)) (succ u3)} (Equiv.{succ (max u1 u3), succ u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (fun (_x : Equiv.{succ (max u1 u3), succ u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) => (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) -> A) (Equiv.hasCoeToFun.{succ (max u1 u3), succ u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (Equiv.symm.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.decompose.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6))) (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ u3) (succ (max u1 u3))} (AddMonoidHom.{u3, max u1 u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (AddMonoid.toAddZeroClass.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (AddCommMonoid.toAddMonoid.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.addCommMonoid.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))))) (fun (_x : AddMonoidHom.{u3, max u1 u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (AddMonoid.toAddZeroClass.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (AddCommMonoid.toAddMonoid.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.addCommMonoid.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))))) => (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) -> (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (AddMonoidHom.hasCoeToFun.{u3, max u1 u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (AddMonoid.toAddZeroClass.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (AddCommMonoid.toAddMonoid.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (AddMonoid.toAddZeroClass.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (AddCommMonoid.toAddMonoid.{max u1 u3} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.addCommMonoid.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))))) (DirectSum.of.{u1, u3} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i) (coeFn.{succ (max u1 u3), max (succ u1) (succ u3)} (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u3} ι (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (fun (_x : DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u3} ι (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) => forall (i : ι), coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u1, u3, u3} ι (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) a i)))
+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : DecidableEq.{succ u3} ι] [_inst_2 : AddMonoid.{u3} ι] [_inst_3 : CommSemiring.{u1} R] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u3, u1, u2} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] (a : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) (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} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (fun (a : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => A) a) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.decompose.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6))) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_3) (CommSemiring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R A A (CommSemiring.toSemiring.{u1} R _inst_3) (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3)))) (GradedAlgebra.proj.{u3, u1, u2} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 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} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (fun (_x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.decompose.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6))) a)) (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} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (fun (_x : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) => A) _x) (Equiv.instFunLikeEquiv.{max (succ u3) (succ u2), succ u2} (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) A) (Equiv.symm.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) (DirectSum.decompose.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u3, u2, u2} ι A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (AddMonoidHom.{u2, max u2 u3} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))) ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (_x : (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) => DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) _x) (AddHomClass.toFunLike.{max u3 u2, u2, max u3 u2} (AddMonoidHom.{u2, max u2 u3} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))) ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddZeroClass.toAdd.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)))) (AddZeroClass.toAdd.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))) (AddMonoidHomClass.toAddHomClass.{max u3 u2, u2, max u3 u2} (AddMonoidHom.{u2, max u2 u3} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))) ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)))) (AddMonoidHom.addMonoidHomClass.{u2, max u3 u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddMonoid.toAddZeroClass.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))) (AddMonoid.toAddZeroClass.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (AddCommMonoid.toAddMonoid.{max u3 u2} (DirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i)) (instAddCommMonoidDirectSum.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i))))))) (DirectSum.of.{u3, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i) i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddCommMonoid.ofSubmonoidOnSemiring.{u3, u2, u2} ι (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) A _inst_4 (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_3 _inst_4 _inst_5)) 𝒜 i) i))) i)) a i)))
+Case conversion may be inaccurate. Consider using '#align graded_algebra.proj_recompose GradedAlgebra.proj_recomposeₓ'. -/
 theorem GradedAlgebra.proj_recompose (a : ⨁ i, 𝒜 i) (i : ι) :
     GradedAlgebra.proj 𝒜 i ((decompose 𝒜).symm a) = (decompose 𝒜).symm (of _ i (a i)) := by
   rw [GradedAlgebra.proj_apply, decompose_symm_of, Equiv.apply_symm_apply]
 #align graded_algebra.proj_recompose GradedAlgebra.proj_recompose
 
+/- warning: graded_algebra.mem_support_iff -> GradedAlgebra.mem_support_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : AddMonoid.{u1} ι] [_inst_3 : CommSemiring.{u2} R] [_inst_4 : Semiring.{u3} A] [_inst_5 : Algebra.{u2, u3} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] [_inst_7 : DecidableEq.{succ u3} A] (r : A) (i : ι), Iff (Membership.Mem.{u1, u1} ι (Finset.{u1} ι) (Finset.hasMem.{u1} ι) i (Dfinsupp.support.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => AddZeroClass.toHasZero.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i)))) (fun (i : ι) (x : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) => Ne.decidable.{succ u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (fun (a : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (b : coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) => Subtype.decidableEq.{u3} A (fun (x : A) => Membership.Mem.{u3, u3} A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.hasMem.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i)) (fun (a : A) (b : A) => _inst_7 a b) a b) x (OfNat.ofNat.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) 0 (OfNat.mk.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) 0 (Zero.zero.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (AddZeroClass.toHasZero.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (AddMonoid.toAddZeroClass.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i)))))))) (coeFn.{max 1 (max (succ u3) (succ (max u1 u3))) (succ (max u1 u3)) (succ u3), max (succ u3) (succ (max u1 u3))} (Equiv.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (fun (_x : Equiv.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) => A -> (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (Equiv.hasCoeToFun.{succ u3, succ (max u1 u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u3)} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5))) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (DirectSum.decompose.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u1, u3, u3} ι A (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6)) r))) (Ne.{succ u3} A (coeFn.{succ u3, succ u3} (LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) (fun (_x : LinearMap.{u2, u2, u3, u3} R R (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5)) => A -> A) (LinearMap.hasCoeToFun.{u2, u2, u3, u3} R R A A (CommSemiring.toSemiring.{u2} R _inst_3) (CommSemiring.toSemiring.{u2} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u2, u3} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_3)))) (GradedAlgebra.proj.{u1, u2, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 i) r) (OfNat.ofNat.{u3} A 0 (OfNat.mk.{u3} A 0 (Zero.zero.{u3} A (MulZeroClass.toHasZero.{u3} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))))))))
+but is expected to have type
+  forall {ι : Type.{u2}} {R : Type.{u1}} {A : Type.{u3}} [_inst_1 : DecidableEq.{succ u2} ι] [_inst_2 : AddMonoid.{u2} ι] [_inst_3 : CommSemiring.{u1} R] [_inst_4 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u3} R A _inst_3 _inst_4] (𝒜 : ι -> (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) [_inst_6 : GradedAlgebra.{u2, u1, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜] [_inst_7 : DecidableEq.{succ u3} A] (r : A) (i : ι), Iff (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i (Dfinsupp.support.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 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} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i))) (fun (i : ι) (x : Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) => instDecidableNot (Eq.{succ u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) x (OfNat.ofNat.{u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) 0 (Zero.toOfNat0.{u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i)))))) (Subtype.instDecidableEqSubtype.{u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i)) (fun (a : A) (b : A) => _inst_7 a b) x (OfNat.ofNat.{u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) 0 (Zero.toOfNat0.{u3} ((fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) (AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)) i))))))) (FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (Equiv.{succ u3, max (succ u3) (succ u2)} A (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u2) (succ u3)} A (DirectSum.{u2, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (SetLike.instMembership.{u3, u3} (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5))) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (𝒜 i)))) (DirectSum.decompose.{u2, u3, u3} ι A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 (GradedRing.toDecomposition.{u2, u3, u3} ι A (Submodule.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_4 (Submodule.setLike.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) (Submodule.addSubmonoidClass.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) 𝒜 _inst_6)) r))) (Ne.{succ u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) r) (FunLike.coe.{succ u3, succ u3, succ u3} (LinearMap.{u1, u1, u3, u3} R R (CommSemiring.toSemiring.{u1} R _inst_3) (CommSemiring.toSemiring.{u1} R _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3))) A A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, u3} R R A A (CommSemiring.toSemiring.{u1} R _inst_3) (CommSemiring.toSemiring.{u1} R _inst_3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_4))) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5) (Algebra.toModule.{u1, u3} R A _inst_3 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_3)))) (GradedAlgebra.proj.{u2, u1, u3} ι R A (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 _inst_3 _inst_4 _inst_5 𝒜 _inst_6 i) r) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) r) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) r) (MonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) r) (Semiring.toMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : A) => A) r) _inst_4)))))
+Case conversion may be inaccurate. Consider using '#align graded_algebra.mem_support_iff GradedAlgebra.mem_support_iffₓ'. -/
 theorem GradedAlgebra.mem_support_iff [DecidableEq A] (r : A) (i : ι) :
     i ∈ (decompose 𝒜 r).support ↔ GradedAlgebra.proj 𝒜 i r ≠ 0 :=
   Dfinsupp.mem_support_iff.trans Submodule.coe_eq_zero.Not.symm
@@ -256,6 +358,7 @@ variable [CanonicallyOrderedAddMonoid ι]
 
 variable [SetLike σ A] [AddSubmonoidClass σ A] (𝒜 : ι → σ) [GradedRing 𝒜]
 
+#print GradedRing.projZeroRingHom /-
 /-- If `A` is graded by a canonically ordered add monoid, then the projection map `x ↦ x₀` is a ring
 homomorphism.
 -/
@@ -292,11 +395,18 @@ def GradedRing.projZeroRingHom : A →+* A
     · rintro _ _ ha hb _
       simp only [add_mul, decompose_add, add_apply, AddMemClass.coe_add, ha, hb]
 #align graded_ring.proj_zero_ring_hom GradedRing.projZeroRingHom
+-/
 
 variable {a b : A} {n i : ι}
 
 namespace DirectSum
 
+/- warning: direct_sum.coe_decompose_mul_of_left_mem_of_not_le -> DirectSum.coe_decompose_mul_of_left_mem_of_not_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : Semiring.{u2} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u3, u2} σ A] [_inst_5 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {n : ι} {i : ι}, (Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) a (𝒜 i)) -> (Not (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n)) -> (Eq.{succ u2} A ((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 A _inst_4) (𝒜 n)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 n)))))) (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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) a b)) n)) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))))))
+but is expected to have type
+  forall {ι : Type.{u1}} {A : Type.{u3}} {σ : Type.{u2}} [_inst_1 : Semiring.{u3} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u2, u3} σ A] [_inst_5 : AddSubmonoidClass.{u2, u3} σ A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {n : ι} {i : ι}, (Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) a (𝒜 i)) -> (Not (LE.le.{u1} ι (Preorder.toLE.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n)) -> (Eq.{succ u3} A (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u2, u3} σ A _inst_4 (𝒜 n))) (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} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u3, u3, u3} A A A (instHMul.{u3} A (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1)))) a b)) n)) (OfNat.ofNat.{u3} A 0 (Zero.toOfNat0.{u3} A (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_left_mem_of_not_le DirectSum.coe_decompose_mul_of_left_mem_of_not_leₓ'. -/
 theorem coe_decompose_mul_of_left_mem_of_not_le (a_mem : a ∈ 𝒜 i) (h : ¬i ≤ n) :
     (decompose 𝒜 (a * b) n : A) = 0 :=
   by
@@ -304,6 +414,12 @@ theorem coe_decompose_mul_of_left_mem_of_not_le (a_mem : a ∈ 𝒜 i) (h : ¬i
   rwa [decompose_mul, decompose_coe, coe_of_mul_apply_of_not_le]
 #align direct_sum.coe_decompose_mul_of_left_mem_of_not_le DirectSum.coe_decompose_mul_of_left_mem_of_not_le
 
+/- warning: direct_sum.coe_decompose_mul_of_right_mem_of_not_le -> DirectSum.coe_decompose_mul_of_right_mem_of_not_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : Semiring.{u2} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u3, u2} σ A] [_inst_5 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {n : ι} {i : ι}, (Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) b (𝒜 i)) -> (Not (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n)) -> (Eq.{succ u2} A ((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 A _inst_4) (𝒜 n)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 n)))))) (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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) a b)) n)) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))))))
+but is expected to have type
+  forall {ι : Type.{u1}} {A : Type.{u3}} {σ : Type.{u2}} [_inst_1 : Semiring.{u3} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u2, u3} σ A] [_inst_5 : AddSubmonoidClass.{u2, u3} σ A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {n : ι} {i : ι}, (Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) b (𝒜 i)) -> (Not (LE.le.{u1} ι (Preorder.toLE.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n)) -> (Eq.{succ u3} A (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u2, u3} σ A _inst_4 (𝒜 n))) (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} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u3, u3, u3} A A A (instHMul.{u3} A (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1)))) a b)) n)) (OfNat.ofNat.{u3} A 0 (Zero.toOfNat0.{u3} A (MonoidWithZero.toZero.{u3} A (Semiring.toMonoidWithZero.{u3} A _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_right_mem_of_not_le DirectSum.coe_decompose_mul_of_right_mem_of_not_leₓ'. -/
 theorem coe_decompose_mul_of_right_mem_of_not_le (b_mem : b ∈ 𝒜 i) (h : ¬i ≤ n) :
     (decompose 𝒜 (a * b) n : A) = 0 :=
   by
@@ -313,6 +429,12 @@ theorem coe_decompose_mul_of_right_mem_of_not_le (b_mem : b ∈ 𝒜 i) (h : ¬i
 
 variable [Sub ι] [OrderedSub ι] [ContravariantClass ι ι (· + ·) (· ≤ ·)]
 
+/- warning: direct_sum.coe_decompose_mul_of_left_mem_of_le -> DirectSum.coe_decompose_mul_of_left_mem_of_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : Semiring.{u2} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u3, u2} σ A] [_inst_5 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {n : ι} {i : ι} [_inst_7 : Sub.{u1} ι] [_inst_8 : OrderedSub.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))) _inst_7] [_inst_9 : ContravariantClass.{u1, u1} ι ι (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))))) (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))))], (Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) a (𝒜 i)) -> (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n) -> (Eq.{succ u2} A ((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 A _inst_4) (𝒜 n)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 n)))))) (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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) a b)) n)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) a ((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 A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n 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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) b) (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i)))))
+but is expected to have type
+  forall {ι : Type.{u1}} {A : Type.{u3}} {σ : Type.{u2}} [_inst_1 : Semiring.{u3} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u2, u3} σ A] [_inst_5 : AddSubmonoidClass.{u2, u3} σ A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {n : ι} {i : ι} [_inst_7 : Sub.{u1} ι] [_inst_8 : OrderedSub.{u1} ι (Preorder.toLE.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) (AddZeroClass.toAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))) _inst_7] [_inst_9 : ContravariantClass.{u1, u1} ι ι (fun (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3010 : ι) (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3012 : ι) => HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))))) x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3010 x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3012) (fun (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3025 : ι) (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3027 : ι) => LE.le.{u1} ι (Preorder.toLE.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3025 x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3027)], (Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) a (𝒜 i)) -> (LE.le.{u1} ι (Preorder.toLE.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n) -> (Eq.{succ u3} A (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u2, u3} σ A _inst_4 (𝒜 n))) (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} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u3, u3, u3} A A A (instHMul.{u3} A (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1)))) a b)) n)) (HMul.hMul.{u3, u3, u3} A A A (instHMul.{u3} A (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1)))) a (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u2, u3} σ A _inst_4 (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n 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} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) b) (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i)))))
+Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_left_mem_of_le DirectSum.coe_decompose_mul_of_left_mem_of_leₓ'. -/
 theorem coe_decompose_mul_of_left_mem_of_le (a_mem : a ∈ 𝒜 i) (h : i ≤ n) :
     (decompose 𝒜 (a * b) n : A) = a * decompose 𝒜 b (n - i) :=
   by
@@ -320,6 +442,12 @@ theorem coe_decompose_mul_of_left_mem_of_le (a_mem : a ∈ 𝒜 i) (h : i ≤ n)
   rwa [decompose_mul, decompose_coe, coe_of_mul_apply_of_le]
 #align direct_sum.coe_decompose_mul_of_left_mem_of_le DirectSum.coe_decompose_mul_of_left_mem_of_le
 
+/- warning: direct_sum.coe_decompose_mul_of_right_mem_of_le -> DirectSum.coe_decompose_mul_of_right_mem_of_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : Semiring.{u2} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u3, u2} σ A] [_inst_5 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {n : ι} {i : ι} [_inst_7 : Sub.{u1} ι] [_inst_8 : OrderedSub.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))) _inst_7] [_inst_9 : ContravariantClass.{u1, u1} ι ι (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))))) (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))))], (Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) b (𝒜 i)) -> (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n) -> (Eq.{succ u2} A ((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 A _inst_4) (𝒜 n)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 n)))))) (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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) a b)) n)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) ((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 A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n 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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) a) (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) b))
+but is expected to have type
+  forall {ι : Type.{u1}} {A : Type.{u3}} {σ : Type.{u2}} [_inst_1 : Semiring.{u3} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u2, u3} σ A] [_inst_5 : AddSubmonoidClass.{u2, u3} σ A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {n : ι} {i : ι} [_inst_7 : Sub.{u1} ι] [_inst_8 : OrderedSub.{u1} ι (Preorder.toLE.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) (AddZeroClass.toAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))) _inst_7] [_inst_9 : ContravariantClass.{u1, u1} ι ι (fun (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3183 : ι) (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3185 : ι) => HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))))) x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3183 x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3185) (fun (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3198 : ι) (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3200 : ι) => LE.le.{u1} ι (Preorder.toLE.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3198 x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3200)], (Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) b (𝒜 i)) -> (LE.le.{u1} ι (Preorder.toLE.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n) -> (Eq.{succ u3} A (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u2, u3} σ A _inst_4 (𝒜 n))) (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} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u3, u3, u3} A A A (instHMul.{u3} A (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1)))) a b)) n)) (HMul.hMul.{u3, u3, u3} A A A (instHMul.{u3} A (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1)))) (Subtype.val.{succ u3} A (fun (x : A) => Membership.mem.{u3, u3} A (Set.{u3} A) (Set.instMembershipSet.{u3} A) x (SetLike.coe.{u2, u3} σ A _inst_4 (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n 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} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u1, u3} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u3, max (succ u1) (succ u3)} A (DirectSum.{u1, u3} ι (fun (i : ι) => Subtype.{succ u3} A (fun (x : A) => Membership.mem.{u3, u2} A σ (SetLike.instMembership.{u2, u3} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u3, u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u3, u2} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) a) (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) b))
+Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_right_mem_of_le DirectSum.coe_decompose_mul_of_right_mem_of_leₓ'. -/
 theorem coe_decompose_mul_of_right_mem_of_le (b_mem : b ∈ 𝒜 i) (h : i ≤ n) :
     (decompose 𝒜 (a * b) n : A) = decompose 𝒜 a (n - i) * b :=
   by
@@ -327,6 +455,12 @@ theorem coe_decompose_mul_of_right_mem_of_le (b_mem : b ∈ 𝒜 i) (h : i ≤ n
   rwa [decompose_mul, decompose_coe, coe_mul_of_apply_of_le]
 #align direct_sum.coe_decompose_mul_of_right_mem_of_le DirectSum.coe_decompose_mul_of_right_mem_of_le
 
+/- warning: direct_sum.coe_decompose_mul_of_left_mem -> DirectSum.coe_decompose_mul_of_left_mem is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : Semiring.{u2} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u3, u2} σ A] [_inst_5 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {i : ι} [_inst_7 : Sub.{u1} ι] [_inst_8 : OrderedSub.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))) _inst_7] [_inst_9 : ContravariantClass.{u1, u1} ι ι (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))))) (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))))] (n : ι) [_inst_10 : Decidable (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n)], (Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) a (𝒜 i)) -> (Eq.{succ u2} A ((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 A _inst_4) (𝒜 n)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 n)))))) (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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) a b)) n)) (ite.{succ u2} A (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n) _inst_10 (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) a ((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 A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n 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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) b) (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i)))) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1)))))))))
+but is expected to have type
+  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : Semiring.{u2} A] [_inst_2 : DecidableEq.{succ u3} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u3} ι] [_inst_4 : SetLike.{u1, u2} σ A] [_inst_5 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {i : ι} [_inst_7 : Sub.{u3} ι] [_inst_8 : OrderedSub.{u3} ι (Preorder.toLE.{u3} ι (PartialOrder.toPreorder.{u3} ι (OrderedAddCommMonoid.toPartialOrder.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))) (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3))))) _inst_7] [_inst_9 : ContravariantClass.{u3, u3} ι ι (fun (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3356 : ι) (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3358 : ι) => HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))))) x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3356 x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3358) (fun (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3371 : ι) (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3373 : ι) => LE.le.{u3} ι (Preorder.toLE.{u3} ι (PartialOrder.toPreorder.{u3} ι (OrderedAddCommMonoid.toPartialOrder.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))) x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3371 x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3373)] (n : ι) [_inst_10 : Decidable (LE.le.{u3} ι (Preorder.toLE.{u3} ι (PartialOrder.toPreorder.{u3} ι (OrderedAddCommMonoid.toPartialOrder.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))) i n)], (Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) a (𝒜 i)) -> (Eq.{succ u2} A (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_4 (𝒜 n))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1)))) a b)) n)) (ite.{succ u2} A (LE.le.{u3} ι (Preorder.toLE.{u3} ι (PartialOrder.toPreorder.{u3} ι (OrderedAddCommMonoid.toPartialOrder.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))) i n) _inst_10 (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1)))) a (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_4 (𝒜 (HSub.hSub.{u3, u3, u3} ι ι ι (instHSub.{u3} ι _inst_7) n i)))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) b) (HSub.hSub.{u3, u3, u3} ι ι ι (instHSub.{u3} ι _inst_7) n i)))) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_left_mem DirectSum.coe_decompose_mul_of_left_memₓ'. -/
 theorem coe_decompose_mul_of_left_mem (n) [Decidable (i ≤ n)] (a_mem : a ∈ 𝒜 i) :
     (decompose 𝒜 (a * b) n : A) = if i ≤ n then a * decompose 𝒜 b (n - i) else 0 :=
   by
@@ -334,6 +468,12 @@ theorem coe_decompose_mul_of_left_mem (n) [Decidable (i ≤ n)] (a_mem : a ∈ 
   rwa [decompose_mul, decompose_coe, coe_of_mul_apply]
 #align direct_sum.coe_decompose_mul_of_left_mem DirectSum.coe_decompose_mul_of_left_mem
 
+/- warning: direct_sum.coe_decompose_mul_of_right_mem -> DirectSum.coe_decompose_mul_of_right_mem is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {A : Type.{u2}} {σ : Type.{u3}} [_inst_1 : Semiring.{u2} A] [_inst_2 : DecidableEq.{succ u1} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u1} ι] [_inst_4 : SetLike.{u3, u2} σ A] [_inst_5 : AddSubmonoidClass.{u3, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {i : ι} [_inst_7 : Sub.{u1} ι] [_inst_8 : OrderedSub.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))) _inst_7] [_inst_9 : ContravariantClass.{u1, u1} ι ι (HAdd.hAdd.{u1, u1, u1} ι ι ι (instHAdd.{u1} ι (AddZeroClass.toHasAdd.{u1} ι (AddMonoid.toAddZeroClass.{u1} ι (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))))))) (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))))] (n : ι) [_inst_10 : Decidable (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n)], (Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) b (𝒜 i)) -> (Eq.{succ u2} A ((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 A _inst_4) (𝒜 n)) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 n)) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 n)))))) (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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) a b)) n)) (ite.{succ u2} A (LE.le.{u1} ι (Preorder.toHasLe.{u1} ι (PartialOrder.toPreorder.{u1} ι (OrderedAddCommMonoid.toPartialOrder.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3)))) i n) _inst_10 (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) ((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 A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (coeBase.{succ u2, succ u2} (coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u3} A σ (SetLike.hasMem.{u3, u2} σ A _inst_4) x (𝒜 (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n 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 A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) (fun (_x : DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) => forall (i : ι), coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (DirectSum.hasCoeToFun.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 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)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (fun (_x : Equiv.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) => A -> (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (Equiv.hasCoeToFun.{succ u2, succ (max u1 u2)} A (DirectSum.{u1, u2} ι (fun (i : ι) => coeSort.{succ u3, succ (succ u2)} σ Type.{u2} (SetLike.hasCoeToSort.{u3, u2} σ A _inst_4) (𝒜 i)) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u1, u2, u3} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u1} ι (OrderedAddCommMonoid.toAddCommMonoid.{u1} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u1} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) a) (HSub.hSub.{u1, u1, u1} ι ι ι (instHSub.{u1} ι _inst_7) n i))) b) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1)))))))))
+but is expected to have type
+  forall {ι : Type.{u3}} {A : Type.{u2}} {σ : Type.{u1}} [_inst_1 : Semiring.{u2} A] [_inst_2 : DecidableEq.{succ u3} ι] [_inst_3 : CanonicallyOrderedAddMonoid.{u3} ι] [_inst_4 : SetLike.{u1, u2} σ A] [_inst_5 : AddSubmonoidClass.{u1, u2} σ A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))))) _inst_4] (𝒜 : ι -> σ) [_inst_6 : GradedRing.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜] {a : A} {b : A} {i : ι} [_inst_7 : Sub.{u3} ι] [_inst_8 : OrderedSub.{u3} ι (Preorder.toLE.{u3} ι (PartialOrder.toPreorder.{u3} ι (OrderedAddCommMonoid.toPartialOrder.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))) (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3))))) _inst_7] [_inst_9 : ContravariantClass.{u3, u3} ι ι (fun (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3542 : ι) (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3544 : ι) => HAdd.hAdd.{u3, u3, u3} ι ι ι (instHAdd.{u3} ι (AddZeroClass.toAdd.{u3} ι (AddMonoid.toAddZeroClass.{u3} ι (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))))) x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3542 x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3544) (fun (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3557 : ι) (x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3559 : ι) => LE.le.{u3} ι (Preorder.toLE.{u3} ι (PartialOrder.toPreorder.{u3} ι (OrderedAddCommMonoid.toPartialOrder.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))) x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3557 x._@.Mathlib.RingTheory.GradedAlgebra.Basic._hyg.3559)] (n : ι) [_inst_10 : Decidable (LE.le.{u3} ι (Preorder.toLE.{u3} ι (PartialOrder.toPreorder.{u3} ι (OrderedAddCommMonoid.toPartialOrder.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))) i n)], (Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) b (𝒜 i)) -> (Eq.{succ u2} A (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_4 (𝒜 n))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1)))) a b)) n)) (ite.{succ u2} A (LE.le.{u3} ι (Preorder.toLE.{u3} ι (PartialOrder.toPreorder.{u3} ι (OrderedAddCommMonoid.toPartialOrder.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3)))) i n) _inst_10 (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1)))) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u1, u2} σ A _inst_4 (𝒜 (HSub.hSub.{u3, u3, u3} ι ι ι (instHSub.{u3} ι _inst_7) n i)))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Dfinsupp.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) ι (fun (_x : ι) => (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) _x) (Dfinsupp.funLike.{u3, u2} ι (fun (i : ι) => (fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (fun (i : ι) => (fun (i : ι) => AddMonoid.toZero.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) (AddCommMonoid.toAddMonoid.{u2} ((fun (i : ι) => (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) i) i) ((fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)) i))) i)) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (Equiv.{succ u2, max (succ u2) (succ u3)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) A (fun (_x : A) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : A) => DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i))) _x) (Equiv.instFunLikeEquiv.{succ u2, max (succ u3) (succ u2)} A (DirectSum.{u3, u2} ι (fun (i : ι) => Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u1} A σ (SetLike.instMembership.{u1, u2} σ A _inst_4) x (𝒜 i))) (fun (i : ι) => AddSubmonoidClass.toAddCommMonoid.{u2, u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) σ _inst_4 _inst_5 (𝒜 i)))) (DirectSum.decompose.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_1))) _inst_4 _inst_5 𝒜 (GradedRing.toDecomposition.{u3, u2, u1} ι A σ (fun (a : ι) (b : ι) => _inst_2 a b) (AddCommMonoid.toAddMonoid.{u3} ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} ι (CanonicallyOrderedAddMonoid.toOrderedAddCommMonoid.{u3} ι _inst_3))) _inst_1 _inst_4 _inst_5 𝒜 _inst_6)) a) (HSub.hSub.{u3, u3, u3} ι ι ι (instHSub.{u3} ι _inst_7) n i))) b) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align direct_sum.coe_decompose_mul_of_right_mem DirectSum.coe_decompose_mul_of_right_memₓ'. -/
 theorem coe_decompose_mul_of_right_mem (n) [Decidable (i ≤ n)] (b_mem : b ∈ 𝒜 i) :
     (decompose 𝒜 (a * b) n : A) = if i ≤ n then decompose 𝒜 a (n - i) * b else 0 :=
   by

70fd9563

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -272,10 +272,10 @@ def GradedRing.projZeroRingHom : A →+* A
     rfl
   map_mul' := by
     refine' DirectSum.Decomposition.inductionOn 𝒜 (fun x => _) _ _
-    · simp only [zero_mul, decompose_zero, zero_apply, ZeroMemClass.coe_zero]
+    · simp only [MulZeroClass.zero_mul, decompose_zero, zero_apply, ZeroMemClass.coe_zero]
     · rintro i ⟨c, hc⟩
       refine' DirectSum.Decomposition.inductionOn 𝒜 _ _ _
-      · simp only [mul_zero, decompose_zero, zero_apply, ZeroMemClass.coe_zero]
+      · simp only [MulZeroClass.mul_zero, decompose_zero, zero_apply, ZeroMemClass.coe_zero]
       · rintro j ⟨c', hc'⟩
         · simp only [Subtype.coe_mk]
           by_cases h : i + j = 0
@@ -285,8 +285,8 @@ def GradedRing.projZeroRingHom : A →+* A
               decompose_of_mem_same 𝒜 (show c' ∈ 𝒜 0 from (add_eq_zero_iff.mp h).2 ▸ hc')]
           · rw [decompose_of_mem_ne 𝒜 (mul_mem hc hc') h]
             cases' show i ≠ 0 ∨ j ≠ 0 by rwa [add_eq_zero_iff, not_and_or] at h with h' h'
-            · simp only [decompose_of_mem_ne 𝒜 hc h', zero_mul]
-            · simp only [decompose_of_mem_ne 𝒜 hc' h', mul_zero]
+            · simp only [decompose_of_mem_ne 𝒜 hc h', MulZeroClass.zero_mul]
+            · simp only [decompose_of_mem_ne 𝒜 hc' h', MulZeroClass.mul_zero]
       · intro _ _ hd he
         simp only [mul_add, decompose_add, add_apply, AddMemClass.coe_add, hd, he]
     · rintro _ _ ha hb _

70fd9563

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

70fd9563

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

@@ -48,7 +48,6 @@ variable {ι R A σ : Type*}
 section GradedRing
 
 variable [DecidableEq ι] [AddMonoid ι] [CommSemiring R] [Semiring A] [Algebra R A]
-
 variable [SetLike σ A] [AddSubmonoidClass σ A] (𝒜 : ι → σ)
 
 open DirectSum
@@ -130,7 +129,6 @@ section AddCancelMonoid
 open DirectSum
 
 variable [DecidableEq ι] [Semiring A] [SetLike σ A] [AddSubmonoidClass σ A] (𝒜 : ι → σ)
-
 variable {i j : ι}
 
 namespace DirectSum
@@ -166,7 +164,6 @@ end AddCancelMonoid
 section GradedAlgebra
 
 variable [DecidableEq ι] [AddMonoid ι] [CommSemiring R] [Semiring A] [Algebra R A]
-
 variable (𝒜 : ι → Submodule R A)
 
 /-- A special case of `GradedRing` with `σ = Submodule R A`. This is useful both because it
@@ -260,9 +257,7 @@ section CanonicalOrder
 open SetLike.GradedMonoid DirectSum
 
 variable [Semiring A] [DecidableEq ι]
-
 variable [CanonicallyOrderedAddCommMonoid ι]
-
 variable [SetLike σ A] [AddSubmonoidClass σ A] (𝒜 : ι → σ) [GradedRing 𝒜]
 
 /-- If `A` is graded by a canonically ordered add monoid, then the projection map `x ↦ x₀` is a ring

70fd9563

fix(RingTheory/GradedAlgebra/Basic): rewrite simps lemma by hand (#7574)

The simps lemmas generated here were bad. The porting note matches the one on decomposeAddEquiv which also needed manual lemmas.

This also adds new lemmas that help keep simp confluent.

953f84aa

Diff

@@ -202,7 +202,7 @@ namespace DirectSum
 
 /-- If `A` is graded by `ι` with degree `i` component `𝒜 i`, then it is isomorphic as
 an algebra to a direct sum of components. -/
-@[simps!]
+-- Porting note: deleted [simps] and added the corresponding lemmas by hand
 def decomposeAlgEquiv : A ≃ₐ[R] ⨁ i, 𝒜 i :=
   AlgEquiv.symm
     { (decomposeAddEquiv 𝒜).symm with
@@ -210,6 +210,24 @@ def decomposeAlgEquiv : A ≃ₐ[R] ⨁ i, 𝒜 i :=
       commutes' := (coeAlgHom 𝒜).commutes }
 #align direct_sum.decompose_alg_equiv DirectSum.decomposeAlgEquiv
 
+@[simp]
+lemma decomposeAlgEquiv_apply (a : A) :
+    decomposeAlgEquiv 𝒜 a = decompose 𝒜 a := rfl
+
+@[simp]
+lemma decomposeAlgEquiv_symm_apply (a : ⨁ i, 𝒜 i) :
+    (decomposeAlgEquiv 𝒜).symm a = (decompose 𝒜).symm a := rfl
+
+@[simp]
+lemma decompose_algebraMap (r : R) :
+    decompose 𝒜 (algebraMap R A r) = algebraMap R (⨁ i, 𝒜 i) r :=
+  (decomposeAlgEquiv 𝒜).commutes r
+
+@[simp]
+lemma decompose_symm_algebraMap (r : R) :
+    (decompose 𝒜).symm (algebraMap R (⨁ i, 𝒜 i) r) = algebraMap R A r :=
+  (decomposeAlgEquiv 𝒜).symm.commutes r
+
 end DirectSum
 
 open DirectSum

70fd9563

chore: rename CanonicallyOrderedAddMonoid to ..AddCommMonoid (#7503)

Renames:

CanonicallyOrderedMonoid -> CanonicallyOrderedCommMonoid

CanonicallyOrderedAddMonoid -> CanonicallyOrderedAddCommMonoid

CanonicallyLinearOrderedMonoid -> CanonicallyLinearOrderedCommMonoid

CanonicallyLinearOrderedAddMonoid -> CanonicallyLinearOrderedAddCommMonoid

f3bc24c3

Diff

@@ -243,7 +243,7 @@ open SetLike.GradedMonoid DirectSum
 
 variable [Semiring A] [DecidableEq ι]
 
-variable [CanonicallyOrderedAddMonoid ι]
+variable [CanonicallyOrderedAddCommMonoid ι]
 
 variable [SetLike σ A] [AddSubmonoidClass σ A] (𝒜 : ι → σ) [GradedRing 𝒜]

70fd9563

perf: remove overspecified fields (#6965)

This removes redundant field values of the form add := add for smaller terms and less unfolding during unification.

A list of all files containing a structure instance of the form { a1, ... with x1 := val, ... } where some xi is a field of some aj was generated by modifying the structure instance elaboration algorithm to print such overlaps to stdout in a custom toolchain.

Using that toolchain, I went through each file on the list and attempted to remove algebraic fields that overlapped and were redundant, eg add := add and not toFun (though some other ones did creep in). If things broke (which was the case in a couple of cases), I did not push further and reverted.

It is possible that pushing harder and trying to remove all redundant overlaps will yield further improvements.

12150475

Diff

@@ -74,8 +74,7 @@ a ring to a direct sum of components. -/
 def decomposeRingEquiv : A ≃+* ⨁ i, 𝒜 i :=
   RingEquiv.symm
     { (decomposeAddEquiv 𝒜).symm with
-      map_mul' := (coeRingHom 𝒜).map_mul
-      map_add' := (coeRingHom 𝒜).map_add }
+      map_mul' := (coeRingHom 𝒜).map_mul }
 #align direct_sum.decompose_ring_equiv DirectSum.decomposeRingEquiv
 
 @[simp]
@@ -208,7 +207,6 @@ def decomposeAlgEquiv : A ≃ₐ[R] ⨁ i, 𝒜 i :=
   AlgEquiv.symm
     { (decomposeAddEquiv 𝒜).symm with
       map_mul' := (coeAlgHom 𝒜).map_mul
-      map_add' := (coeAlgHom 𝒜).map_add
       commutes' := (coeAlgHom 𝒜).commutes }
 #align direct_sum.decompose_alg_equiv DirectSum.decomposeAlgEquiv

70fd9563

chore: drop MulZeroClass. in mul_zero/zero_mul (#6682)

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

277dea95

Diff

@@ -268,10 +268,10 @@ def GradedRing.projZeroRingHom : A →+* A where
     rfl
   map_mul' := by
     refine' DirectSum.Decomposition.inductionOn 𝒜 (fun x => _) _ _
-    · simp only [MulZeroClass.zero_mul, decompose_zero, zero_apply, ZeroMemClass.coe_zero]
+    · simp only [zero_mul, decompose_zero, zero_apply, ZeroMemClass.coe_zero]
     · rintro i ⟨c, hc⟩
       refine' DirectSum.Decomposition.inductionOn 𝒜 _ _ _
-      · simp only [MulZeroClass.mul_zero, decompose_zero, zero_apply, ZeroMemClass.coe_zero]
+      · simp only [mul_zero, decompose_zero, zero_apply, ZeroMemClass.coe_zero]
       · rintro j ⟨c', hc'⟩
         · simp only [Subtype.coe_mk]
           by_cases h : i + j = 0
@@ -281,8 +281,8 @@ def GradedRing.projZeroRingHom : A →+* A where
               decompose_of_mem_same 𝒜 (show c' ∈ 𝒜 0 from (add_eq_zero_iff.mp h).2 ▸ hc')]
           · rw [decompose_of_mem_ne 𝒜 (SetLike.GradedMul.mul_mem hc hc') h]
             cases' show i ≠ 0 ∨ j ≠ 0 by rwa [add_eq_zero_iff, not_and_or] at h with h' h'
-            · simp only [decompose_of_mem_ne 𝒜 hc h', MulZeroClass.zero_mul]
-            · simp only [decompose_of_mem_ne 𝒜 hc' h', MulZeroClass.mul_zero]
+            · simp only [decompose_of_mem_ne 𝒜 hc h', zero_mul]
+            · simp only [decompose_of_mem_ne 𝒜 hc' h', mul_zero]
       · intro _ _ hd he
         simp only at hd he -- Porting note: added
         simp only [mul_add, decompose_add, add_apply, AddMemClass.coe_add, hd, he]

70fd9563

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

@@ -43,7 +43,7 @@ graded algebra, graded ring, graded semiring, decomposition
 
 open DirectSum BigOperators
 
-variable {ι R A σ : Type _}
+variable {ι R A σ : Type*}
 
 section GradedRing

70fd9563

chore: fix names (Add)SubmonoidClass.Subtype (#6374)

f6bf5e04

Diff

@@ -103,7 +103,7 @@ end DirectSum
 
 /-- The projection maps of a graded ring -/
 def GradedRing.proj (i : ι) : A →+ A :=
-  (AddSubmonoidClass.Subtype (𝒜 i)).comp <|
+  (AddSubmonoidClass.subtype (𝒜 i)).comp <|
     (DFinsupp.evalAddMonoidHom i).comp <|
       RingHom.toAddMonoidHom <| RingEquiv.toRingHom <| DirectSum.decomposeRingEquiv 𝒜
 #align graded_ring.proj GradedRing.proj

70fd9563

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser, Kevin Buzzard, Jujian Zhang
-
-! This file was ported from Lean 3 source module ring_theory.graded_algebra.basic
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.DirectSum.Algebra
 import Mathlib.Algebra.DirectSum.Decomposition
 import Mathlib.Algebra.DirectSum.Internal
 import Mathlib.Algebra.DirectSum.Ring
 
+#align_import ring_theory.graded_algebra.basic from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
 /-!
 # Internally-graded rings and algebras

70fd9563

chore: rename Dfinsupp to DFinsupp (#5822)

See #4354

268b7d43

Diff

@@ -107,7 +107,7 @@ end DirectSum
 /-- The projection maps of a graded ring -/
 def GradedRing.proj (i : ι) : A →+ A :=
   (AddSubmonoidClass.Subtype (𝒜 i)).comp <|
-    (Dfinsupp.evalAddMonoidHom i).comp <|
+    (DFinsupp.evalAddMonoidHom i).comp <|
       RingHom.toAddMonoidHom <| RingEquiv.toRingHom <| DirectSum.decomposeRingEquiv 𝒜
 #align graded_ring.proj GradedRing.proj
 
@@ -124,7 +124,7 @@ theorem GradedRing.proj_recompose (a : ⨁ i, 𝒜 i) (i : ι) :
 
 theorem GradedRing.mem_support_iff [∀ (i) (x : 𝒜 i), Decidable (x ≠ 0)] (r : A) (i : ι) :
     i ∈ (decompose 𝒜 r).support ↔ GradedRing.proj 𝒜 i r ≠ 0 :=
-  Dfinsupp.mem_support_iff.trans ZeroMemClass.coe_eq_zero.not.symm
+  DFinsupp.mem_support_iff.trans ZeroMemClass.coe_eq_zero.not.symm
 #align graded_ring.mem_support_iff GradedRing.mem_support_iff
 
 end GradedRing
@@ -221,7 +221,7 @@ open DirectSum
 
 /-- The projection maps of graded algebra-/
 def GradedAlgebra.proj (𝒜 : ι → Submodule R A) [GradedAlgebra 𝒜] (i : ι) : A →ₗ[R] A :=
-  (𝒜 i).subtype.comp <| (Dfinsupp.lapply i).comp <| (decomposeAlgEquiv 𝒜).toAlgHom.toLinearMap
+  (𝒜 i).subtype.comp <| (DFinsupp.lapply i).comp <| (decomposeAlgEquiv 𝒜).toAlgHom.toLinearMap
 #align graded_algebra.proj GradedAlgebra.proj
 
 @[simp]
@@ -237,7 +237,7 @@ theorem GradedAlgebra.proj_recompose (a : ⨁ i, 𝒜 i) (i : ι) :
 
 theorem GradedAlgebra.mem_support_iff [DecidableEq A] (r : A) (i : ι) :
     i ∈ (decompose 𝒜 r).support ↔ GradedAlgebra.proj 𝒜 i r ≠ 0 :=
-  Dfinsupp.mem_support_iff.trans Submodule.coe_eq_zero.not.symm
+  DFinsupp.mem_support_iff.trans Submodule.coe_eq_zero.not.symm
 #align graded_algebra.mem_support_iff GradedAlgebra.mem_support_iff
 
 end GradedAlgebra

70fd9563

chore: remove superfluous parentheses in calls to ext (#5258)

Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

3d6731dc

Diff

@@ -194,7 +194,7 @@ def GradedAlgebra.ofAlgHom [SetLike.GradedMonoid 𝒜] (decompose : A →ₐ[R]
   left_inv := AlgHom.congr_fun right_inv
   right_inv := by
     suffices decompose.comp (DirectSum.coeAlgHom 𝒜) = AlgHom.id _ _ from AlgHom.congr_fun this
-    -- Porting note: was ext (i x) : 2
+    -- Porting note: was ext i x : 2
     refine DirectSum.algHom_ext' _ _ fun i => ?_
     ext x
     exact (decompose.congr_arg <| DirectSum.coeAlgHom_of _ _ _).trans (left_inv i x)

70fd9563

chore: convert lambda in docs to fun (#5045)

Found with git grep -n "λ [a-zA-Z_ ]*,"

1164cf04

Diff

@@ -62,7 +62,7 @@ respects multiplication, i.e. the product of an element of degree `i` and an ele
 is an element of degree `i + j`.
 
 Note that the fact that `A` is internally-graded, `GradedAlgebra 𝒜`, implies an externally-graded
-algebra structure `DirectSum.GAlgebra R (λ i, ↥(𝒜 i))`, which in turn makes available an
+algebra structure `DirectSum.GAlgebra R (fun i ↦ ↥(𝒜 i))`, which in turn makes available an
 `Algebra R (⨁ i, 𝒜 i)` instance.
 -/
 class GradedRing (𝒜 : ι → σ) extends SetLike.GradedMonoid 𝒜, DirectSum.Decomposition 𝒜

70fd9563

feat: port RingTheory.GradedAlgebra.Basic (#4143)

3eaf5985

`ring_theory.graded_algebra.basic` ⟷ `Mathlib.RingTheory.GradedAlgebra.Basic`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 462

ring_theory.graded_algebra.basic ⟷ Mathlib.RingTheory.GradedAlgebra.Basic

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 462

`ring_theory.graded_algebra.basic` ⟷ `Mathlib.RingTheory.GradedAlgebra.Basic`